QA 

53 
?4 


UC-NRLF 

I'l  ill  Ml   ii[{  1 

1  III  1 

N  1 

:  1  ■    1  i    1 
II  mil  II 

111111 

*<:    IbS    775 

4 


THREE    AND    FOUR    PLACE 


TABLES 


ct 


LOGAEITHMTC  AND  TRIGONOMETRIC 


FUNCTIONS 


BT 


JAMES  MILLS  PEIRCE 

mnVEESITT   PEOFESSOR   OF   MATHEMATICS   IN   HARVARD    UNITERSITY 


■v-.,.      ^,, 


^/6^  =  ^J 


BOSTON 

GINN     BROTHERS 

1871 

Entered  according  to  Act  of  Congress,  in  the  year  1871,  by  James  Mills  Pubob, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


^fitli 


PBOPORTIONAL    PARTS. 

S                                              lO 

15 

30 

1 

0.1 

0.2 

0.3 

0.4     0.5 

0.6     0.7     0.8     0.9     1.0 

1.1     1.2 

1.3 

1.4 

1.5 

1,6 

1.7 

1.8 

1.9     2.0 

1 

2 

0.2 

0.4 

0.6 

0.8     1.0 

1.2     1.4     1.6     1.8     2.0 

2.2     2.4 

2.6 

2.8 

3.0 

3.2 

3.4 

3.6 

3.8     4.0 

2 

3 

0.3 

0.6 

0.9 

1.2     1.5 

1.8     2.1     2.4     2.7    3.0 

3.3     3.6 

3.9 

4.2 

4.5 

4.8 

5.1 

5,4 

5.7     6.0 

3 

4 

0.4 

0.8 

1.2 

1.6     2.0 

2.4     2.8     3.2     3.6     4.0 

4.4     4.8 

5.2 

5.6 

6.0 

6.4 

6.8 

7.2 

7.6     8.0 

4 

5 

0.5 

1.0 

1.5 

2.0     2.5 

3.0     3.5     4.0     4.5     5.0 

5.5     6.0 

6.5 

7.0 

7.5 

8.0 

8.5 

9.0 

9.5  10.0 

5 

6 

0.6 

1.2 

1.8 

2.4     3.0 

3.6     4.2     4.8     5.4     6.0 

6.6     7.2 

7.8 

8.4 

9.0 

9.6 

10,2 

10.8 

11.4  12.0 

6 

7 

0.7 

1.4 

2.1 

2.8     3.5 

4.2     4.9     5.6     6.3     7.0 

7.7     8.4 

9.1 

9.8 

10.5 

11.2 

11.9 

12.6 

13.3  14,0 

7 

8 

0.8 

1.6 

2.4 

3.2     4.0 

4.8     5.6     6.4     7.2     8.0 

8.8     9.6 

10.4 

11.2 

12.0 

12.8 

13.6 

14.4 

15.2  16.0 

8 

9 

0.9 

1.8 

2.7 

3.6     4.5 

5.4     6.3     7.2     8.1     9.0 

9.9  10.8 

11.7 

12.6 

13.5 

14.4 

15.3 

16.2 

17.1  18.0 

9 

35                                              30 

35 

40 

1 

2.1 

2.2 

2.3 

2.4     2.5 

2.6     2.7     2.8     2.9     3.0 

3.1     3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

3.8 

3.9     4.0 

1 

2 

4.2 

4.4 

4.6 

4.8     5.0 

5.2     5.4     5.6     5.8     6.0 

6.2     6.4 

6.6 

6.8 

7.0 

7.2 

7.4 

7.6 

7.8     8.0 

2 

3 

6.3 

6.6 

6.9 

7.2     7.5 

7.8     8.1     8.4     8.7     9.0 

9.3     9.6 

9.9 

10.2 

10.5 

10.8 

11.1 

11.4 

11.7  12.0 

3 

4 

8.4 

8.8 

9.2 

9.6  10.0 

10.4  10.8  11.2  11.6  12.0 

12.4  12.8 

13.2 

13.6 

14.0 

14.4 

14.8 

15.2 

15.6  16.0 

4 

5 

10.5 

11.0 

11,5 

12.0  12.5 

13.0  13.5  14.0  14.5  15.0 

15.5  16.0 

16.5 

17.0 

17.5 

18.0 

18.5 

19.0 

19.5  20.0 

5 

6 

12.6 

13.2 

13.8 

14.4  15.0 

15.6  16.2  16.8  17.4   18.0 

18.6  19.2 

19.8 

20.4 

21.0 

21.6 

22.2 

22.8 

23.4  24.0 

6 

7 

14.7 

15.4 

16.1 

16.8  17.5 

18.2  18.9  19.6  20.3  21.0 

21.7  22.4 

23.1 

23.8 

24.5 

25.2 

25.9 

26.6 

27.3  28.0 

7 

8 

16.8 

17.6 

18.4 

19.2  20.0 

20.8  21.6  22.4  23.2  24.0 

24.8  25.6 

26.4 

27.2 

28.0 

28.8 

29.6 

30.4 

31.2  32.0 

8 

9 

18.9 

19.8 

20.7 

21.6  22.5 

23.4  24.3  25.2  26.1  27.0 

27.9  28.8 

29.7 

30.6 

31.5 

32,4 

33.3 

34.2 

35.1  36.0 

9 

45                                              SO 

55 

60 

1 

4.1 

4.2 

4.3 

4.4    4.5 

4.6     4.7     4.8     4.9     5.0 

5.1     5.2 

5.3 

5.4 

5.5 

5.6 

5.7 

5.8 

5.9     6.0 

1 

2 

8.2 

8.4 

8.6 

8.8    9.0 

9.2     9.4     9.6     9.8  10.0 

10.2  10.4 

10.6 

10.8 

11.0 

11.2 

11.4 

11.6 

11.8  12.0 

2 

3 

12.3 

12.6 

12.9 

13.2  13.5 

13.8  14.1   14.4  14.7  15.0 

15.3  15.6 

15.9 

16.2 

16.5 

16.8 

17.1 

17.4 

17.7  18.0 

3 

4 

16.4 

16.8 

17.2 

17.6  18.0 

18.4  18.8  19.2  19.6  20.0 

20.4  20.8 

21.2 

21.6 

22.0 

22.4 

22.8 

23.2 

23.6  24.0 

4 

5 

20.5 

21.0 

21.5 

22.0  22.5 

23.0  23.5  24.0  24.5  25.0 

25.5  26.0 

26.5 

27.0 

27.5 

28.0 

28.5 

29.0 

29.5  30.0 

5 

6 

24.6 

25.2 

25.8 

26.4  27.0 

27.6  28.2  28.8  29.4  30.0 

30.6  31.2 

31.8 

32.4 

33.0 

33.6 

34,2 

34.8 

35.4  30.0 

6 

7 

28.7 

29.4 

30.1 

30.8  31.5 

32.2  32.9  33.6  34.3  35.0 

35.7  36.4 

37.1 

37.8 

38.5 

39.2 

39.9 

40.6 

41.3  42.0 

7 

8 

32.8 

33.6 

34.4 

35.2  36.0 

36.8  37.6  38.4  39.2  40.0 

40.8  41.6 

42.4 

43.2 

44.0 

44.8 

45.6 

46.4 

47.2  48.0 

8 

9 

36.9 

37.8 

38.7 

39.6  40.5 

41.4  42.3  43.2  44.1  45.0 

45.9  46.8 

47.7 

48.6 

49.5 

50.4 

51.3 

52.2 

53.1   54.0 

9 

65                                   yo 

75 

SO 

1 

6.1 

6.2 

6.3 

6.4     6.5 

6.6     6.7     6.8     6.9     7.0 

7.1     7.2 

7.3 

7.4 

7.5 

7.6 

7.7 

7.8 

7.9     8.0 

1 

2 

12.2 

12.4 

12.6 

12.8  13.0 

13.2  13.4  13.6  13.8  14.0 

14.2   14.4 

14.6 

14.8 

15.0 

15.2 

15.4 

15.6 

15.8  16.0 

2 

3 

18.3 

18.6 

18.9 

19.2  19.5 

19.8  20.1  20.4  20.7  21.0 

21.3  21.6 

21.9 

22.2 

22.5 

22.8 

23.1 

23.4 

23.7  24.0 

3 

4 

24.4 

24.8 

25.2 

25.6  26.0 

26.4  26.8  27.2  27.6  28.0 

28.4  28.8 

29.2 

29.6 

30.0 

30.4 

30.8 

31.2 

31.6  32.0 

4 

5 

30.5 

31.0 

31.5 

32.0  32.5 

33.0  33.5  34.0  34.5  35.0 

35.5  36.0 

36.5 

37.0 

37.5 

38.0 

38.5 

39.0 

39.5  40.0 

5 

6 

36.6 

37.2 

37.8 

38.4  39.0 

39.6  40.2  40.8  41.4  42.0 

42.6  43.2 

43.8 

44.4 

45.0 

45.6 

46.2 

46.8 

47.4  48.0 

6 

7 

42.7 

43.4 

44.1 

44.8  45.5 

46.2  46.9  47.6  48.3  49.0 

49.7  50.4 

51.1 

51.8 

52.5 

53.2 

53.9 

54.6 

55.3  56.0 

7 

8 

48.8 

49.6 

50.4 

51.2  52.0 

52.8  53.6  54.4  55.2  56.0 

56.8  57.6 

58.4 

59.2 

60.0 

60.8 

61.6 

62.4 

63.2  64.0 

8 

9 

54.9 

55.8 

56.7 

57.6  58.J5 

59.4  60.3  61.2  62.1  63.0 
....       •    • 

63.9  64.8 

65.7 

66.6 

67.5 

68.4 

69.3 

70.2 

71.1  72.0 

9 

05 

lOO 

1 

8.1 

8.2 

8.3 

8A\  S|5>" 

:  §j;:*»*.7jf8.8:  M   k-o 

9.1     9.2 

9.3 

9.4 

9.5 

9.6 

9.7 

9.8 

9.9  10.0 

1 

2 

16.2 

16.4 

16.6 

16.8  "iVIo 

f7.S'l7.4"ir.6*  17.8*16.0 

18.2  18.4 

18.6 

18.8 

19.0 

19.2 

19.4 

19.6 

19.8  20.0 

2 

3 

24.3 

24.6 

24.9 

25.2  25.5 

25.8  26.1  26.4  26.7  27.0 

27.3  27.6 

27.9 

28.2 

28.5 

28.8 

29.1 

29.4 

29.7  30.0 

3 

4 

32.4 

32.8 

33.2 

33.6  34.0 

34.4  34.8  35.2  35.6  36.0 

36.4  36.8 

37.2 

37.6 

38.0 

38.4 

38,8 

39.2 

39.0  40.0 

4 

5 

40.5 

41.0 

41.5 

42.0  42.5 

43.0  43.5  44.0  44.5  45.0 

45.5  46.0 

46.5 

47.0 

47.5 

48.0 

48.5 

49.0 

49.5  50.0 

5 

6 

48.6 

49.2 

49.8 

50.4  51.0 

51.0  52.2  52.8  53.4  54.0 

54.6  55.2 

55.8 

56.4 

57.0 

57.6 

58.2 

58.8 

59.4  00.0 

6 

7 

56.7 

57.4 

58.1 

58.8  59.5 

60.2  60.9  61.6  62.3  63.0 

63.7  64.4 

65.1 

65.8 

66.5 

67.2 

67.9 

68.6 

69.3  70.0 

/ 

8 

64.8 

65.6 

66.4 

67.2  68.0 

68.8  69.6  70.4  71.2  72.0 

72.8  73.6 

74.4 

75.2 

76.0 

76.8 

77.6 

78.4 

79.2  80.0 

8 

9 

72.9 

73.8 

74.7 

75.6  76.5 

77.4  78.3  79.2  80.1  81.0 

81.9  82.8 

83.7 

84.6 

85.5 

86.4 

87.3 

88.2 

89.1  90.0 

9 

THREE-PLACE 

TABLES. 

LOGAKITUMS 

OF  Numbers. 

lo 

gsinqp 

= 

l0g((jp 

in 

degrees)  -|-  S 

log  tan  (f 
9 

"~~" 

log  (9 

5 

IQ 

degrees)  -f-  T 
qp          T 

O           1           3           3           4 

9 

«           7           8 

9 

lO 

1 

000      041      079 

114  i     146 

176 

204 

230 

255      279 

301 

3 

301      322      342 

362 

380 

398 

415 

431 

447      462 

477 

8.242 

3 

477      491      505 

519 

531 

544 

556 

568 

580      591 

602 

3°  .82 

4 

602      613      623 

633 

643 

653 

663 

672 

681      690 

699 

4°  .01 

S 

e 

699      708      716 

724 

732 

740 

748 

756 

763      771 

778 

8.-241 

6°.12 

8.243 

8.244 

778      785      792 

799 

806 

813 

820 

826 

833      839 

845 

T 

845      851      857 

863 

869 

875 

881 

886 

892      898 

903 

7°. 83 

7°.  70 

8 

903      908      914 

919 

924 

929 

934 

940 

944      949 

954 

8.245 

9 

954      959      964 

968 

973 

978 

982 

987 

991      996 

000 

■ 

9    .04 

8.246 

lO 

000      004      009 

013      017 

021 

025 

029 

033      037 

041 

10    .3S 

0°.20 

LOGAKITIIXIIC 

Natural 

0 

sin            CSC        tan           ctn 

sec 

cos 

sin 

CSC 

tan 

ctn 

sec 

COS 

1 

8.242        1.758    8.242        1.758 1 

0.000 

0.000 

0.017 

57.30 

0.017 

57.29 

1.000 

1.000 

1 

89 

f 

.543          .457 

.543          .457 

.000 

0.000 

.035  '* 

28.65 

.035 

28.64 

.001 

0.999 

88 

8 

.719          .281 

.719          .281 

.001 

9.999 

.052  " 

19.11 

.052 

19.08 

.001 

.999 

1 

87 

4 

.844           .156 

.845          .155 

.001 

.999 

.070   '* 

14.34 

.070 

14.30 

.002 

.998 

86 

5 
0 

8.940         1.060 

8.942        1.058 

.002 

.998 

.087  " 

11.47 

.087 

-18 

11.43 

.004 

■  2 

.996 

1 

86. 
84 

9.019        0.981 

9.022        0.978 

.002 

.998 

.105     ■ 

9.57 

.105 

9.51 

.006 

.995 

7 

.086          .914 

.089          .911 

.003 

.997 

.122  " 

8.21 

.123 

8.14' 

.008 

.993 

83 

8 

.144          .856 

.148          .852 

.004 

.996 

.139  " 

7.19 

.141 

7.12 

.010 

.990 

82 

9 

.194          .806 

.200          .800 

.005 

.995 

.156-" 

6.39 

.158 

6.31 

.012 

.988 

81 

10 

.240          .760 

.246          .754 

.007 

.993 

.174   " 

5.76 

.176 

5.67 

.015 

.985 

80 

11 

.281          .719 

.289          .711 

.008 

.992 

.191 

5.24 

.194 

5.14 

.019 

.982 

79 

12 

.318  "     .682 

.327  ^     .673 

.010 

.990 

.208   " 

4.81 

.213 

4.70 

.022 

.978 

78 

1ft 

.352  '•*     .648 

.363  '*     .637 

.011 

.989 

.225  " 

4.45 

aa 

.231 

4.33 

3; 

.026 

4 

.974 

4 

77 

14 

.384  ^     .616 

.397  ^     .603 

.013 

.987 

.242  '■' 

4.13 

»a 

.249 

4.01 

.031 

.970 

76 

15 

.413  ^'     .587 

.428  "     .572 

.015 

.985 

.259   " 

3.80 

ai 

.268 

-10 

3.73 

■^1 

.035 

4 

.  5 

.966 

"i 

75 

16 

.440          .560 

.457          .543 

.017 

.983 

.276 

3.G3 

.287 

3.49 

.040 

.961 

74 

17 

.466  ^*     .534 

.485  **     .515 

.019 

.981 

.292   '" 

3.42 

ai 

.306 

3.27 

.046 

6 

.956 

5 

73 

IS 

.490  ^     .510 

.512  "     .488 

.022 

.978 

.309   '" 

3.24 

18 

.325 

19 

3.08 

19 

.051 

b 

.951 

5 

72 

19 

.513  *'     .487 

.537  ^     .403 

.024 

.976 

.326   " 

3.07 

I'i 

.344 

la 

2.90 

18 

.058 

■I 

.946 

6 

71 

20 

.534   ^'     .466 

.561   **     .439 

.027 

.973 

.342  " 

2.92 

15 

.364 

2.75 

15 

11 

.064 

6 

.940 

6 

70 

21 

.554           .446 

.584           .416 

.030 

.970 

.358 

2.79 

.384 

2.61 

.071 

.934 

69 

22 

.574  ^     .426 

.606  ^^     .394 

.033 

.967 

.375  " 

2.67 

.404 

2.48 

.079 

.927 

'; 

68 

23 

.592  '*     .408 

.628  ^*     .372 

.036 

.964 

.391   '" 

2.56 

11 

.424 

'M 

2.36 

I'J 

.086 

7 

.921 

6 

67 

24 

.609  "     .391 

.649  ^'     .351 

.039 

.961 

.407  '' 

2.46 

10 

.445 

!il 

2.25 

11 

.095 

9 

.914 

7 

66 

25 

.026   "     .374 

.669  ^     .331 

.043 

.957 

.423   "* 

2.37 

9 

.466 

iil 

2.14 

11 

.103 

8 

.906 

8 

65 

26 

.642          .358 

.688           .312 

.046 

.954 

.438 

2.28 

.488 

2.05 

.113 

.899 

64 

27 

.657   '^     .343 

.707  "     .293 

.050 

.950 

.454   " 

2.20 

.510 

1.96 

.122 

.891 

8 

63 

28 

.672  '*     .328 

.726  '*     .274 

.054 

.946 

.469  '' 

2.13 

7 

.532 

W 

1.88 

8 

.133 

11 

.883 

8 

62 

29 

.686   '*     .314 

.744   '*     .256 

.058 

.942 

.485  " 

2.06 

J 

.554 

1.80 

.143 

.875 

8 

61 

30 

.699   "     .301 

.761    "     .239 

.062 

.938 

.500   " 

2.00 

.577 

1.73 

.155 

.866 

•  9 

60 

31 

.712          .288 

.779    °     .221 

.067 

.933 

.515 

1.94 

.601 

1.66 

.167 

.857 

59 

32 

.724   "     .276 

.796  "     .204 

.072 

.928 

.530   '^ 

1.89 

b 

.625 

•2i 

1.60 

0 

.179 

12 

.848 

9 

58 

33 

.730   '*     .264 

.813  "     .187 

.076 

.924 

.545   '= 

1.84 

b 

.649 

1.54 

ii 

.192 

13 

.839 

9 

57 

34 
35 

.748   "     .252 
.7.59   "     .241 

.829   '*     .171 

.081 

.919 

.559   " 

.     15 

1.79 

5 

.675 

2.1 

1.48 

A 

.206 

Mi 

.829 

m 

56 
55 

.845   '^     .155 

.087 

.913 

.574 

1.74 

.700 

1.43 

.221 

.819 

36 

.769          .231 

.861           .139 

.092 

.908 

.588- 

1.70 

.727 

1.38 

.236 

.809 

54 

37 

.779   '»     .221 

.877   '*     .123 

.098 

.902 

.602   " 

1.66 

.754 

1.33 

S 

.252 

IB 

.799 

10 

53 

38 

.789   '"     .211 

.893   '*     .107 

.103 

.897 

.616   '" 

1.62 

.781 

'■ti 

1.28 

6 

.269 

11 

.788 

11 

52 

39 

.799   '"     .201 

.908  '*     .092 

.109 

.891 

.629   '^ 

1.59 

.810 

1.23 

6 

.287 

18 

.777 

11 

51 

40 
41 

.808     ^     .192 

.924   '*     .076 

.116 

.884 

.043  " 

1.56 

.  4 

.839 

..30 

1.19 

4 
■  4 

.305 

18 
-20 

.766 

11 
11 

50 
49 

.817           .183 

.939          .061 

.122 

.878 

.656 

1.52 

.869 

1.15 

.325 

.755 

42 

.826    "     .174 

.954   '*     .046 

.129 

.871 

.669   " 

1.49 

.900 

31 

1.11 

4 

.346 

21 

.743 

12 

48 

43 

.834    *     .166 

.970   '*     .030 

.136 

.864 

.682  " 

1.47 

.933 

33 

1.07 

4 

.367 

21 

.731 

12 

47 

44 

.842    *     .158 

9.985  "     .015 

.143 

.857 

.695  " 

1.44 

0.966 

1.04 

3 

.390 

23 

.719 

12 

46 

45 

9.849     '  0.151 

0.000   '*  0.000 

0.151 

9.849 

0.707   '^ 

1.41 

1.000 

1.00 

4 

1.414 

24 

0.707 

12 

45 

cos            sec        ctn           tan 

CSC 

sin 

cos 

sec 

Ctn 

tan 

CSC 

sin 

0 

Logarithmic 

Nati 

JRAL 



4273«4 


LOGARITHMS 

OF 

NUMBERS. 

Proportional 

Parts. 

t 

O 

1 

2 

3 

4 

s 

6 

7 

8 

9 

•< 

^g 

1 

3 

3 

4 

s 

6 

7 

8 

» 

lO 

1  40 

~io 

0000 

043 

086 

128 

170 

212 

253 

294 

334 

374 

4.1 

8.3 

12.4 

10.6 

20.7 

34.8 

29.0 

33.1 

37.3 

41.4 

50 

11 

414 

453 

492 

531 

569 

607 

645 

682 

719 

755 

3.8 

7.6 

11.3 

16.1 

18.9 

32.7 

26.5 

30.3 

34.0 

37.8 

2  00 

12 

792 

828 

864 

899 

934 

969 

o04 

o38 

o72 

i06 

3.5 

7.0 

10.4 

13.9 

17.4 

20.9 

34.3 

37.8 

31.3 

34.8 

10 

13 

1139 

173 

206 

239 

271 

303 

335 

367 

399 

430 

3.3 

6.4 

9.7 

13.9 

16.1 

19.3 

22.5 

36.7 

39.0 

33.2 

20 
30 

14 
15 

461 

492 

523 

553 

584 

614 

644 

673 

703 

732 

3.0 

6.0 

9.0 

12.0 

15.0 

18.0 

31.0 

34.0 

37.0 

30.0 

1761 

790 

818 

847 

875 

903 

931 

959 

987 

014 

3.8 

6.6 

8.4 

11.2 

14.0 

16.8 

19.6 

33.4 

25.2 

28.0 

40 

16 

2041 

068 

095 

122 

148 

175 

201 

227 

253 

279 

3.8 

6.3 

7.9 

10.5 

13.3 

16.8 

18.4 

31.1 

23.7 

96.3 

50 

17 

304 

330 

355 

380 

405 

430 

455 

480 

504 

529 

3.S 

6.0 

7.4 

9.9 

13.4 

14.9 

17.4 

19.9 

23.3 

24.8 

3  00 

18 

553 

577 

601 

625 

648 

672 

695 

718 

742 

765 

3.3 

4.7 

7.0 

9.4 

11.7 

14.1 

16.4 

18.8 

21.1 

23.5 

10 
80 

19 
20 

788 

810 

833 

856 

878 

900 

923 

945 

967 

989 

3.3 

4.5 

6.7 

8.9 

11.1 

13.4 

15.6 

17.8 

20.0 

23.3 

3010 

032 

054 

075 

096 

118 

139 

160 

181 

201 

3.1 

4,2 

6.4 

8.6 

10.6 

12.7 

14.8 

17.0 

19.1 

21.2 

30 

21 

222 

243 

263 

284 

304 

324 

345 

365 

385 

404 

3.0 

4.0 

6.1 

8.1 

10.1 

13.1 

14.1 

16.3 

18.2 

20.2 

40 

22 

424 

444 

464 

483 

502 

522 

541 

560 

579 

598 

1.9 

3.9 

6.8 

7.7 

9.7 

11.6 

13.5 

15.4 

17.4 

19.3 

50 

23 

617 

636 

655 

674 

692 

711 

729 

747 

766 

784 

1.8 

3.7 

6.6 

7.4 

9.3 

11.1 

13.9 

14.8 

16.6 

18.5 

4  00 
10 

24 
25 

802 

820 

838 

856 

874 

892 

909 

927 

945 

962 

1.8 

3.5 

5.3 

7.1 

8.9 

10.6 

12.4 

14.3 

16.0 

17.7 

3979 

997 

ol4 

o31 

o48 

o65 

o82 

o99 

il6 

i33 

1.7 

3.4 

6.1 

6.8 

8.6 

10.3 

11.9 

13.6 

16.3 

17.0 

20 

26 

4150 

166 

183 

200 

216 

232 

249 

865 

281 

298 

1.6 

3.3 

4.9 

6.6 

8.3 

9.8 

11.5 

13.1 

14.8 

16.4 

30 

27 

314 

330 

346 

362 

378 

393 

409 

425 

440 

456 

1.6 

8.3 

4.7 

6.3 

7.9 

9.6 

11.1 

13.6 

14.2 

15.8 

40 

28 

472 

487 

502 

518 

533 

548 

564 

579 

594 

609 

1.6 

3.0 

4.6 

6.1 

7.6 

9.1 

10.7 

12.2 

13.7 

16.2 

50 
5  00 

29 
30 

624 

639 

654 

669 

683 

698 

713 

728 

748 

757 

1.5 

3.9 

4.4 

5.9 

7.4 

8.8 

10.3 

11.8 

13.3 

14.7 

4771 

786 

800 

814 

829 

843 

857 

871 

886 

900 

1.4 

2.8 

4.3 

5.7 

7.1 

8.6 

10.0 

11.4 

13.8 

14.2 

10 

31 

914 

928 

942 

955 

969 

983 

997 

oil 

o24 

o38 

1.4 

3.8 

4.1 

6.5 

6.9 

8.3 

9.7 

11.0 

13.4 

13.8 

20 

32 

5051 

065 

079 

092 

105 

119 

132 

145 

159 

172 

1.3 

2.7 

4.0 

5.3 

6.7 

8.0 

9.4 

10.7 

13.0 

13.4 

30 

33 

185 

198 

211 

224 

237 

250 

863 

276 

889 

302 

1.3 

2.6 

3.9 

6.3 

6.5 

7.8 

9.1 

10.4 

11.7 

13.0 

40 
50 

34 
35 

315 

328 

340 

353 

366 

378 

391 

403 

416 

428 

1.3 

3.5 

3.8 

5.0 

6.3 

7.6 

8.8 

10.1 

11.3 

12.6 

5441 

453 

465 

478 

490 

502 

514 

587 

539 

551 

1.2 

3.4 

3.7 

4.9 

6.1 

7.3 

8.6 

9.8 

11.0 

12.2 

6  00 

36 

563 

575 

587 

599 

611 

623 

635 

647 

658 

670 

1.3 

3.4 

3.6 

4.8 

5.9 

7.1 

8.3 

9.6 

10.7 

11.9 

10 

37 

682 

694 

705 

717 

729 

740 

752 

763 

775 

786 

1.2 

3.3 

3.6 

4.6 

5.8 

6.9 

8.1 

9.3 

10.4 

11.6 

20 

38 

798 

809 

821 

838 

843 

855 

866 

877 

888 

899 

1.1 

3.3 

3.4 

4.6 

5.6 

6.8 

7.9 

9.0 

10.3 

11.3 

30 
40 

39 
40 

911 

922 

933 

944 

955 

966 

977 

988 

999 

olO 

I.l 

3.3 

3.3 

4.4 

5.6 

6.6 

7.7 

8.8 

9.9 

11.0 

6021 

031 

042 

053 

064 

075 

085 

096 

107 

117 

1.1 

3.1 

3.3 

4.3 

5.4 

6.4 

7.6 

8.6 

9.7 

10.7 

50 

41 

128 

138 

149 

160 

170 

180 

191 

801 

812 

822 

1.0 

3.1 

3.1 

4.3 

5.3 

6.3 

7.3 

8.4 

9.4 

10.5 

7  00 

42 

232 

243 

853 

263 

274 

284 

294 

304 

314 

385 

1.0 

3.0 

3.1 

4.1 

5.1 

6.1 

7.9 

8.2 

9.2 

10.2 

10 

43 

335 

345 

355 

365 

375 

385 

395 

405 

415 

425 

1.0 

3.0 

a.o 

4.0 

6.0 

6.0 

7.0 

8.0 

9.0 

10.0 

20 
30 

44 
45 

435 

444 

454 

464 

474 

484 

493 

503 

513 

522 

1.0 

2.0 

3.9 

3.9 

4.9 

5.9 

6.8 

7.8 

8.8 

9.8 

6532 

542 

551 

561 

571 

580 

590 

599 

609 

618 

I.O 

1.9 

2.9 

3.8 

4.8 

6.7 

6.7 

7.6 

8.6 

9.5 

40 

46 

628 

637 

646 

656 

665 

675 

684 

693 

708 

712 

0.9 

1.9 

3.8 

8.7 

4.7 

6.6 

6.6 

7.5 

8.4 

9.3 

50 

47 

721 

730 

739 

749 

758 

767 

776 

785 

794 

803 

0.9 

1.8 

3.7 

3.7 

4.6 

6.5 

6.4 

7.3 

8.2 

9.1 

8  00 

48 

612 

821 

830 

839 

848 

857 

866 

875 

884 

893 

0.9 

1.8 

2.7 

3.6 

4.6 

8.4 

6.3 

7.3 

8.1 

9.0 

10 
20 

49 
50 

902 

911 

920 

928 

937 

946 

955 

964 

972 

981 

0.9 

1  8 

3.6 

3.5 

4.4 

5.3 

6.1 

7.0 

7.9 

8.8 

6990 

998 

o07 

ol6 

o24 

o33 

o42 

o50 

o59 

o67 

0.9 

1.7 

2.6 

3.4 

4.3 

6.2 

6.0 

6.9 

7.7 

8.6 

30 

51 

7076 

084 

093 

101 

110 

118 

126 

135 

143 

152 

0.8 

1.7 

2.6 

3.4 

4.3 

6.1 

6.9 

6.7 

7.6 

8.4 

40 

52 

160 

168 

177 

185 

193 

202 

210 

218 

226 

235 

0.8 

1.7 

2.6 

3.3 

4.1 

6.0 

6.8 

6.6 

7.4 

8.3 

50 

53 

243 

251 

259 

267 

275 

284 

292 

300 

308 

316 

0.8 

1.6 

2.4 

3.3 

4.1 

4.9 

6.7 

6.8 

7.3 

8.1 

9  00 

54 

324 

332 

340 

348 

356 

364 

372 

380 

388 

396 

0.8 

1.6 

3.4 

3.2 

4.0 

4.8 

6.6 

6.4 

7.2 

8.0 

log 

arc  (f 

=  log  (ip  in  minut 

es)  +  6.4637 

+  lo 

g  radius. 

log 

9 

o 

0  (X 

1  8 
9  4 

3  3< 

4  0" 

sin  (f 

=  log  (()p  in  D 

linut 

es)  +  S. 

CD 

1.5    "■■'«" 
6.4636 
).6 

6.4634 

r.8 

O     1 
4  07.8 

4  38.8 
6  06.7 
6  33.3 

5  56.0 

S 
6. 4633 
6.4633 
6.4631 
6.4630 

LOGARITHMS 

OF 

NUMBERS. 

J 

II 

Proportional 

Parts. 

0 

1 

3 

3 

4 

S     6 

7 

8 

9 

■< 

'^i 

t 

3 

3 

4 

s 

6 

7 

8 

» 

lO 

9  10 

55 

7404 

412 

419 

427 

435 

443    451 

459 

466 

474 

0.8 

1.6 

2.3 

3.1 

3.9 

4.7 

5.5 

t%3 

7.0 

7.8 

20 

56 

482 

490 

497 

505 

513 

520    528 

536 

543 

551 

0.8 

1.5 

2.3 

3.1 

3.8 

4.6 

5.4 

6.1 

6.9 

7.7 

30 

57 

559 

5C6 

574 

582 

589 

597    604 

612 

619 

627 

0.8 

1.6 

2.3 

3.0 

3.8 

4.5 

6.3 

6.0 

6.8 

7.6 

40 

58 

G34 

642 

649 

657 

664 

672    679 

686 

694 

701 

0.7 

1.6 

2.2 

3.0 

3.7 

4.5 

5.2 

5.9 

6.7 

7.4 

50 
10  00 

59 

60 

709 

716 

723 

731 

738 

745    752 

760 

767 

774 

0.7 

1.5 

2.2 

2.9 

3.6 

4.4 

5.1 

5.9 

6.6 

7.3 

7782 

789 

796 

803 

810 

818    825 

832 

839 

846 

0.7 

1.4 

2.2 

2.9 

3.6 

4.3 

5.0 

6.7 

6.6 

7.2 

10 

61 

853 

860 

868 

875 

882 

889     896 

903 

910 

917 

0.7 

1.4 

2.1 

2.8 

3.5 

4.2 

4.9 

5.6 

6.4 

7.1 

20 

62 

924 

931 

938 

945 

952 

959    966 

973 

980 

987 

0.7 

1.4 

2.1 

2.8 

3.5 

4.2 

4,9 

5.6 

6.3 

6.9 

30 

63 

993 

oOO 

o07 

ul4 

o21 

o28     o35 

o41 

o48 

o55 

0.7 

1.4 

2.1 

2.7 

3.4 

4.1 

4.8 

6.5 

6.2 

6.6 

40 
50 

64 
65 

80G2 

069 

075 

082 

089 

096     102 

109 

116 

122 

0.7 

1.3 

2.0 

2.7 

3.4 

4.0 

4.7 

5.4 

6.1 

0.7 

8129 

136 

142 

149 

156 

162    169 

176 

182 

189 

0.7 

1.3 

2.0 

2.7 

3.3 

4.0 

4.6 

5.3 

6.0 

6.6 

1100 

66 

195 

202 

209 

215 

222 

228    235 

241 

248 

254 

0.7 

1.3 

2.0 

2.6 

3.3 

3.9 

4.6 

5.2 

5.9 

6.5 

10 

67 

2G1 

267 

274 

280 

287 

293    299 

306 

312 

319 

0.6 

1.3 

1.9 

2.6 

3.2 

3.9 

4.5 

5.1 

5.8 

6.4 

20 

68 

325 

331 

338 

344 

351 

357     363 

370 

376 

382 

0.6 

1.3 

1.9 

2.5 

3.2 

3.6 

4.4 

5.1 

6.7 

6.3 

30 
40 

69 
70 

388 

395 

401 

407 

414 

420    426 

432 

439 

445 

0.6 

1.2 

1.9 

2.6 

3.1 

3.7 

4.4 

5.0 

5.6 

6.2 

8451 

457 

463 

470 

476 

482    488 

494 

500 

506 

0.6 

1.2 

1.8 

2.5 

3.1 

3.7 

4.3 

4.9 

6.5 

6.2 

50 

71 

513 

519 

525 

531 

537 

543    549 

555 

561 

567 

0.6 

1.2 

1.8 

2.4 

3.0 

3.6 

4.3 

4.9 

6.6 

6.1 

12  00 

72 

573 

579 

585 

591 

597 

603    609 

615 

621 

627 

0.6 

1.2 

1.8 

2.4 

3.0 

3.6 

4.2 

4.8 

5.4 

6.0 

10 

73 

633 

639 

645 

651 

657 

663    669 

675 

681 

686 

0.6 

1.2 

1.8 

2.4 

3.0 

3.6 

4.1 

4.7 

5.3 

6.9 

20 
30 

74 
75 

692 

698 

704 

710 

716 

722    727 

733 

739 

745 

0.6 

1.2 

1.7 

2.3 

2.9 

3.5 

4.1 

4.7 

5.2 

5.8 

8751 

756 

762 

,768 

774 

779    785 

791 

797 

802 

0.6 

1.2 

1.7 

2.3 

2.9 

3.6 

4.0 

4.6 

5.2 

5.8 

40 

76 

808 

814 

820 

825 

831 

837    842 

848 

854 

859 

0.6 

1.1 

1.7 

2.3 

2.3 

3.4 

4.0 

4.5 

6.1 

5.7 

50 

77 

865 

871 

876 

882 

887 

893    899 

904 

910 

915 

0.6 

1.1 

1.7 

2.2 

2.8 

3.4 

3.9 

4.5 

5.0 

5.6 

13  00 

78 

921 

927 

932 

938 

943 

949    954 

960 

965 

971 

0.6 

1.1 

1.7 

2.2 

2.3 

3.3 

3.9 

4.4 

6.0 

5.5 

10 
20 

79 

80 

976 

982 

987 

993 

998 

o04     o09 

ol5 

o20 

o25 

0.6 

1.1 

1.6 

2.2 

2.7 

3.3 

3.8 

4.4 

4.9 

5.5 

9031 

036 

042 

047 

053 

058     063 

069 

074 

079 

0.5 

1.1 

1.6 

2.2 

2.7 

3.2 

3.8 

4.3 

4.9 

6.4 

30 

81 

oa5 

090 

096 

101 

106 

112     117 

122 

128 

133 

0.5 

1.1 

1.6 

2.1 

2.7 

3.2 

3.7 

4.3 

4.8 

5.3 

1      40 

82 

138 

143 

149 

154 

159 

165    170 

175 

180 

186 

0.5 

l.I 

1.6 

2.1 

2.6 

3.2 

3.7 

4.2 

4.7 

8.3 

!      50 

83 

191 

196 

201 

206 

212 

217    222 

227 

232 

238 

0.5 

1.0 

1.6 

2.1 

2.6 

3.1 

3.6 

4.2 

4.7 

5.2 

14  00 

1       1" 

84 
85 

243 

248 

253 

258 

263 

269    274 

279 

284 

289 

0.4 

1.0 

1.5 

2.1 

2.6 

3.1 

3.6 

4.1 

4.6 

6.1 

9294 

299 

304 

309 

315 

320     325 

330 

335 

340 

0.5 

1.0 

1.6 

2.0 

2.5 

3.0 

3.6 

4.1 

4.6 

5.1 

i      20 

86 

345 

350 

355 

360 

365 

370     375 

380 

385 

390 

0.5 

1.0 

1.6 

2.0 

2.5 

3.0 

3.5 

4.0 

4.6 

5.0 

30 

87 

395 

400 

405 

410 

415 

420    425 

430 

435 

440 

0.5 

I.O 

l.S 

2.0 

2.5 

3.0 

3.5 

4.0 

4.5 

6.0 

40 

88 

445 

450 

455 

460 

465 

469    474 

479 

484 

489 

0.5 

1.0 

1.6 

2.0 

2.5 

2.9 

3.4 

3.9 

4.4 

4.9 

50 
15  00 

89 
90 

494 

499 

504 

509 

513 

518     523 

528 

533 

538 

0.5 

1.0 

1.6 

1.9 

2.4 

2.9 

3.4 

3.9 

4.4 

4.9 

9542 

547 

552 

557 

562 

566    571 

576 

581 

5t-6 

0.5 

1.0 

1.4 

1.9 

2.4 

2.9 

3.4 

3.8 

4.3 

4.8 

10 

91 

590 

595 

600 

605 

609 

614    619 

624 

628 

633 

0.5 

0.9 

1.4 

1.9 

2.4 

2.8 

3.3 

3.8 

4.3 

4.7 

20 

92 

638 

643 

647 

652 

657 

661    666 

671 

675 

680 

0.5 

0.9 

1.4 

1.9 

2.3 

2.6 

3.3 

3.8 

4.2 

4.7 

30 

93 

685 

689 

694 

699 

703 

708    713 

717 

722 

727 

0.5 

0.9 

1.4 

1.9 

2.3 

2.S 

3.3 

3.7 

4.2 

4.6 

40 
50 

94 
95 

731 

736 

741 

745 

750 

754    759 

763 

768 

773 

O.S 

0.9 

1.4 

1.8 

2.3 

2.S 

3.2 

3.7 

4.1 

4.6 

9777 

782 

786 

791 

795 

800     805 

809 

814 

818 

0.5 

0.9 

1.4 

1.8 

2.3 

2.7 

3.2 

3.6 

4.1 

4.5 

IfiOO 

96 

82:} 

827 

832 

836 

841 

845    850 

854 

859 

863 

0.5 

0.9 

1.4 

1.8 

2.3 

2.7 

3.2 

3.6 

4.1 

4.6 

10 

97 

868 

872 

877 

881 

886 

890    894 

899 

903 

908 

0.4 

0.9 

1.3 

1.8 

2.2 

2.7 

3.1 

3.6 

4.0 

4.5 

20 

98 

912 

917 

921 

926 

930 

934    939 

943 

948 

952 

0.4 

0.9 

1.3 

1.8 

2.2 

2.6 

3.1 

3.5 

4.0 

4.4 

30 

99 

956 

961 

965 

969 

974 

978    983 

987 

9!)  I 

996 

0.4 

0.9 

1.3 

1.7 

2.3 

2.6 

3.1 

8.5 

3.9 

4.4 

log  tan  qp  ; 

=  log  ((jp  in  mi 

nutes)  -(- 

r. 

1 

°  '»! 

0  oo.li" 

6. 

0  44.2 

1  40.6 

6. 
9  15. -i 

6. 
5  42.6 

6. 
8  06.0 

<f 

<f 

1 

T 

4637 
163S 
4639 
1640 
4641 

0      <                J. 
3  06.0 

3  26.T    '■^''^ 
6.4643 

3  45.6 

6.4ftl4 

4  03.0 

8.464S 
4  19.3 

6.4646 
4  S4.4 

O      1 
4.34.4 

4  48.S 
8  02.6 

5  15. E 
8  28.4 
8  40.g 

T 

6.4647 
6.4648 
6.4649 
6.4650 
6.4651 

LOGARITHMS   OF  SUMS  AND  DIFFERENCES. 

A 

6.   7.    8.     9.         0.        1.        2.        3. 

A 

6.    7. 

8.    9.        0.        1.         2. 

3. 

B  =  ©A. 

B  =  (SA. 

0.00 

0.00 

0.00 

0.0 

0. 

1. 

2. 

3, 

0.00 

0.00 

0.0 

0. 

0. 

1. 

2. 

8. 

00 

00 

04 

43 

414    9 

3010  60 

0414  91 

0043  99 

0004 

50 

01 

14 

135 

1193  24 

0193  76 

5135  97 

5014 

5001 

01 

0 

4 

4 

23    9 

061  51 

505  91 

142  99 

104 

51 

1 

4 

38 

218   24 

269  76 

232  97 

113 

101 

02 

0 

5 

5 

32    9 

111    61 

596  91 

241  99 

204 

52 

1 

4 

41 

242  26 

346  77 

329  97 

213 

201 

03 

0 

5 

6 

42  10 

163   52 

687  91 

340  99 

304 

53 

1 

5 

45 

267  25 

423  77 

426  97 

313 

301 

04 
05 

0 

5 

7 

52  10 

215   52 

779  92 

439  99 

404 

54 
55 

2 

5 

48 

293  26 

501   78 

523  97 

413 

401 

00 

05 

48 

462  10 

3267  63 

0871  92 

0539  99 

0504 

02 

15 

151 

1319   26 

6578  78 

5621  97 

5512 

5501 

06 

0 

5 

50 

72  10 

321    33 

963  92 

638  99 

604 

56 

2 

6 

55 

345  27 

657  78 

718  97 

612 

601 

07 

5 

1 

82  11 

374  34 

1055  92 

737  99 

704 

57 

2 

6 

58 

372  27 

735  79 

815  97 

712 

701 

08 

5 

2 

93  11 

429  66 

147   92 

836  99 

804 

58 

2 

6 

62 

399  28 

814  79 

913  97 

811 

801 

09 
10 

5 

3 

504  11 

484  65 

239  92 

935  99 

904 

59 
60 

2 

7 

66 

427  28 

893  80 

6010  97 

911 

901 

01 

05 

54 

515  11 

3539  66 

1332  93 

1034  99 

1003 

02 

17 

170 

1455  28 

6973  80 

6108  98 

6011 

6001 

11 

6 

6 

26  11 

595  66 

425  93 

134  99 

103 

61 

2 

8 

73 

484  29 

7053  80 

205  98 

111 

101 

12 

6 

7 

38  12 

652  67 

518   93 

233  99 

203 

62 

2 

8 

77 

513   29 

134  81 

303  98 

210 

201 

13 

6 

8 

50  12 

709  67 

611    93 

332  99 

303 

63 

2 

8 

81 

543  30 

215  81 

401   98 

310 

301 

14 
15 

6 

60 

62  12 

766  68 

704  93 

431  99 

403 

64 
65 

2 

9 

86 

573  30 

296  81 

498  98 

410 

401 

01 

06 

61 

574  )2 

3825  69 

1797  93 

1531  99 

1503 

02 

19 

190 

1604  31 

7377  82 

6596  98 

6510 

6501 

16 

6 

2 

86  13 

884  69 

891    94 

630  99 

603 

66 

2 

20 

94 

635  31 

459  82 

694  98 

609 

601 

17 

6 

4 

99  13 

943  60 

984  94 

729  99 

703 

67 

2 

0 

99 

666  32 

541    82 

792  98 

709 

701 

18 

7 

5 

612  13 

4003  60 

2078  94 

829  99 

803 

68 

2 

1 

203 

699  32 

624  83 

890  98 

809 

801 

19 
20 

7 

7 

25  13 

063  61 

172   94 

928  99 

903 

69 
70 

2 

1 

08 

731  33 

707  83 

988  98 

909 

901 

01 

07 

08 

639  14 

4124  61 

2266  94  2027  99 

2003 

02 

22 

212 

1704  33 

7790  83 

7086  98 

7009 

7001 

21 

7 

70 

53  14 

186  62 

360  94 

127  99 

103 

71 

2 

2 

17 

798  34 

874  84 

184   98 

108 

101 

22 

7 

1 

67  14 

248  62 

454  94 

226  99 

203 

72 

2 

3 

22 

832  34 

957  84 

282  98 

208 

201 

23 

7 

3 

81    16 

311    63 

548  94 

325  99 

303 

73 

2 

3 

27 

867  36 

8042  84 

380  98 

308 

301 

24 
25 

8 

5 

96  15 

374  63 

643  96 

425  99 

402 

74 

75 

2 

4 

32 

902  35 

126   86 

478  96 

408 

401 

01 

08 

77 

711    13 

4438  64 

2738  96  2524  99  2502 

02 

24 

238 

1938  36 

8211    86 

7577  9f 

7508 

7501 

26 

8 

8 

26  15 

502  66 

832  95 

624  99     602 

76 

2 

5 

43 

974  37 

296  83 

675  9E 

608 

601 

27 

8 

80 

42  16 

567  66 

927  96 

723  99 

702 

77 

3 

5 

48 

2011  37 

381    86 

773  96 

707 

701 

28 

8 

2 

57  16 

632  66 

3022  93 

823  99 

802 

78 

3 

6 

54 

048  38 

467  86 

871    96 

807 

801 

29 
30 

8 

4 

74  16 

698  66 

117  95 

922  9!) 

902 

79 

SO 

3 

7 

60 

086  38 

553  86 

970  98 

907 

901 

01 

09 

86 

790  n 

4764  67 

3212  96 

3022  C 

3002 

03 

27 

260 

2124  39 

8639  86 

8068  98 

8007 

8001 

31 

9 

8 

807  n 

831   67 

308  96 

121 

102 

81 

3 

8 

72 

163  39 

725  87 

167  98 

107 

101 

32 

9 

90 

24  n 

899  68 

403  93 

221 

202 

82 

3 

9 

78 

203  40 

812   87 

205  99 

207 

201 

33 

9 

2 

41    18 

966  68 

499  96 

320 

302 

83 

3 

9 

84 

243  40 

899  87 

364  99 

306 

301 

34 
35 

9 

4 

59  18 

5035  69 

594  96    420 

402 

84 
85 

3 

30 

91 

284  41 

986  87 

462  99 

406 

401 

01 

10 

96 

877  18 

5104  69 

3690  96 

3519 

3502 

03 

31 

297 

2325  41 

9074  88 

8561  99 

8506 

8501 

36 

0 

8 

96  19 

173  70 

786  96 

619 

602 

86 

3 

1 

304 

306  42 

162   88 

660  99 

606 

601 

37 

0 

ol 

915  19 

243  70 

881    96 

718 

702 

87 

3 

2 

11 

409  43 

250  88 

758  99 

706 

701 

38 

0 

3 

34  19 

313  71 

977  96 

818 

802 

88 

3 

3 

18 

452  43 

338  88 

857  99 

806 

801 

39 
40 

1 

5 

53  20 

384  71 

4073  96 

918 

902 

89 
90 

3 

4 

25 

495  44 

426  8P 

956  99 

906 

901 

01 

11 

o8 

973  20 

5455  72 

4170  96 

4017 

4002 

03 

34 

332 

2539  44 

9515  89 

9054  99 

9005 

9001 

41 

1 

lO 

93  20 

527  72 

266  96 

117 

102 

91 

4 

5 

39 

584  45 

604  89 

153  99 

105 

101 

42 

1 

3 

0l4   21 

599  72 

362  96 

216 

202 

92 

4 

0 

47 

629  45 

693  89 

252  99 

205 

201 

43 

2 

5 

35  21 

672  73 

458  96 

316 

302 

93 

4 

7 

55 

674  46 

782  89 

351  99 

305 

301 

44 
45 

2 

8 

57  22 

745  73 

555  96 

416 

402 

94 
95 

4 

8 

63 

721  47 

872  90 

450  99 

405 

400 

01 

12 

2l 

078  22 

5819  74 

4651  97  4515 

4502 

04 

39 

371 

2767  47 

9962  90 

9548  99 

9505 

9500 

46 

3 

3 

lOl   22 

893  74 

748  97 

615 

602 

96 

4 

9 

79 

815  48 

0052  90 

647  99 

605 

600 

47 

3 

6 

23   23 

967  76 

845  97 

715 

701 

97 

4 

40 

87 

863  48 

142  90 

746  99 

705 

700 

48 

3 

9 

46  23 

6042  75 

941  97 

814 

801 

98 

4 

1 

96 

911  49 

232  91 

845  99 

805 

800 

49 
50 

3 

32 

69   24 

118  76 

5038  97 

914 

901 

99 
oO 

4       2 

405 

961  49 

323  91 

944  99 

904 

900 

01 

14 

35 

l93   24 

6193  76 

5135  97  5014 

5001 

04      43 

414 

3010  60 

o414  91 

0043  99 

o004 

oOOO 

0.00 

0.00 

0.01 

0.1 

0. 

1.        i    2. 

3. 

0.00    0.00 

0.0 

0. 

1. 

2. 

3. 

4. 

log  {m  -{-  n)  :^  log  n  -|-  ®  (log  m  -\-  arco  log  n). 

log( 

m  —  n) 

=  log  w  -|-  ®"'  (log  m  -\-  arco  1 

og  n). 

log  (a;-}- 1)  =  ®  log  a:=loga;-|-  ®  arco  log  x.    log  (x— 

-1)  = 

:®-Mog: 

c.    log(l — a;)  =  log  a; +  ®"' arco 

logx. 

LOGARITHMTC    TRIGONOMETRIC    FUNCTIONS. 

Angles,      j 

O°  =  0''00" 

10  =  0'"  04°  2°  =  0'08»  3«  =  0''12°    4°  =  0'16»  5°  =  0''20°' 

sec 

m    B 

/ 

sin      tan 

sin      tan            sin      tan            sin     tan            ein      tan            sin     tan 

Angles.                 0.00 

000 
04 

00 
01 

—  00 

8.2419  19  72 

8.5428  31  36 

8.7188  94  24 

8.8436  46  18 

8.9403  20  14 

60 
59 

4  00 
56 

o      /                     00 

0  52.2  89  07.8  "" 

1  30.3  88  29.7  "' 

6.4637  37 

.2490  91  71 

.5464  67  36 

.7212  18  24 

.8454  65  18 

.9417  34  14 

08 

02 

.7648  48 

.2561  62  70 

.5500  03  36 

.7236  42  24 

.8472  83  18 

.9432  49  14 

58 

52 

1  56.6  88  03.4  "z 

12 

0} 

6.9408  08 

.2630  31  69 

.5535  38  35 

.7260  66  24 

.8490  01  18 

.9446  63  14 

57 

48 

2  18.0  87  42.0  "^ 

16 

0  20 

24 

04 
05 
Ofi 

7.0658  58 

.2699  00  68 

.5571  73  35 

.7283  90  24 

.8508  18  18 

.9460  77  14 

56 
55 
54 

44 

3  40 

36 

36.5        23.5  "* 

2  53.0  87  07.0  "^ 

3  08.0  86  52.0  "z 

7.1627  27 

8.2760  67  67 

8.5605  08  35 

8.7307  13  23 

8.8525  36  18 

8.U475  92  14 

.2419  19 

.2832  33  66 

.5640  43  34 

.7330  37  23 

.8543  54  18 

.9489  o6  14 

28 

07 

.3088  88 

.2898  99  65 

.5674  77  34 

.7354  60  23 

.8560  72  18 

.9503  20  14 

53 

32 

22.0        38.0  11 

32 

08 

.3668  68 

.2962  63  64 

.5708  1 1  34 

.7377  83  23 

.8578  89  18 

.9517  34  14 

52 

28 

35.0        25.0  11 

36 

0  40 

44 

09 
10 
11 

.4180  80 

.3025  26  63 

.5742  45  34 

.7400  06  23 

.8595  o7  17 

.9531  49  14 

51 

50 
49 

24 

3  20 

16 

47.3     12.7 ";; 

3  59.0  86  01.0  }, 

4  10.1  85  49.9     ' 
20  7        39  3 

7.4637  37 

8.3088  89  62 

8.5776  79  33 

8.7423  29  23 

8.8613  24  17 

8.9545  63  14 

.5051  51 

.3150  50  61 

.5809  12  33 

.7445  52  23 

.8630  42  n 

.9559  77  14 

48 

12 

.5429  29 

.3210  11  60 

.5842  45  33 

.7468  75  23 

.8647  59  17 

.9573  91  14 

48 

12 

30  9        29  1 

52 

13 

.5777  77 

.3270  71  69 

.5875  78  33 

.7491  97  23 

.8665  76  17 

.9587  05  14 

47 

08 

40  8        19  2 

56 

100 

04 

14 

15 
16 

.6099  99 

.3329  30  69 

.5907  11  32 

.7513  20  22 

.8682  94  17 

.9601  19  14 

46 
45 
44 

04 

3  00 

56 

50.3  09.7  \l 

4  59.5  85  00.5  t^ 

5  08.4  84  51.6  !' 

17.1  42.9    ° 

25.5  34.5  'I 

33.8     26.2  r: 

41.8        18.2  f 

49.6  10.4  ^, 

5  57.3  84  02.7  ,^ 

6  04.8  83  55.2  zt 

12.2  47.8  11 

19.4  40.6  ^; 

26.5    33.5 ;; 

33.4        26.6  Z, 

7.6398  98 

S-.'i.-iSS  89  58 

8.5939  43  33 

8.7535  42  22 

8.8699  11  17 

8.9614  33  14 

.6678  78 

.3445  46  57 

.5972  75  32 

.7557  65  22 

.8716  28  17 

.9628  46  14 

08 

17 

.6942  42 

.3502  03  66 

.6003  07  32 

.7580  87  22 

.8733  45  17 

.9642  60  14 

43 

52 

12 

18 

.7190  90 

.3558  59  56 

.6035  38  31 

.7602  09  22 

.8749  62  17 

.9655  74  14 

42 

48 

16 

120 

24 

19 
20 
21 

.7425  25 

.3613  14  55 

.6066  70  31 

.7623  31  22 

.8766  78  17 

.9669  88  14 

41 
40 
39 

44 

2  40 

36 

7.7648  48 

8.3668  69  54 

8.6097  01  31 

8.7645  52  22 

8.8783  95  n 

8.9682  01  14 

.7859  60 

.3722  23  54 

.6128  32  31 

.7667  74  22 

.8799  l2  17 

.9696  15  14 

28 

22 

.8061  62 

.3775  76  63 

.6159  63  31 

.7688  96  22 

.8816  29  17 

.9709  29  14 

38 

32 

32 

23 

.8255  55 

.3828  29  52 

.6189  93  30 

.7710  17  21 

.8833  45  17 

.9723  42  13 

37 

28 

36 

140 

44 

24 
25 
26 

.8439  39 

.3880  81  52 

.6220  23  30 

.7731  39  21 

.8849  62  16 

.9736  56  13 

36 
35 
34 

24 

2  20 

16 

7.8617  17 

8.3931  32  61 

8.6250  54  30 

8.7752  60  21 

8.8865  78  16 

8.9750  69  13 

.8787  87 

.3982  83  51 

.6279  83  30 

.7773  81  21 

.8882  95  16 

.9763  82  13 

48 

27 

.8951  51 

.4032  33  50 

.6309  13  30 

.7794  02  21 

.8898  11  16 

.9776  96  13 

33 

12 

40.2        19.8  ,„ 

52 

28 

.9109  09 

.4082  83  49 

.6339  43  29 

.7815  23  21 

.8914  27  16 

.9789  09  13 

32 

08 

46.9         1.3.1  f 

56 

2  00 

04 

29 
30 
31 

.9261  61 

.4131  32  49 

.6368  72  29 

.7836  44  21 

.8930  44  16 

.9803  23  13 

31 

30 
29 

04 

2  00 

56 

6  53.5        06.5  ^' 

7  00.0  83  00.0  tt 
06.4  82  53.6  f' 

7.9408  09 

8.4179  81  48 

8.6397  01  29 

8.7857  65  2, 

8.8946  60  16 

8.9816  36  13 

.9551  51 

.4227  29  48 

.6426  30  29 

.7877  86  21 

.8962  76  16 

.9829  49  13 

08 

32 

.9689  89 

.4275  76  47 

.6454  59  29 

.7898  06  20 

.8978  92  16 

.9842  62  13 

28 

52 

\li       '^-^  35 

12 

33 

.9822  23  132 

.4322  23  47 

.6483  87  28 

.7918  27  20 

.8994  08  16 

.9855  75  13 

27 

48 

'^?        *'■"  36 

16 

2  20 

24 

34 
35 
36 

7.9952  52  128 

.4368  70  46 

.651115  28 

.7939  47  20 

.9010  24  16 

.9868  88  13 

26 
25 
24 

44 

140 

36 

25.1        34.9  ,° 
31.1         28.9  ii 
37.1        22.9  ;l 
43.0        17.0 

8.0078  78  m 

8.4414  16  46 

8.6539  44  28 

8.7959  67  20 

8.9026  40  16 

8.9881  01  13 

.0200  00  isi 

.4459  61  45 

.6567  71  28 

.7979  88  20 

.9042  56  16 

.9894  15  13 

28 

37 

.0319  19  117 

.4504  06  45 

.6595  99  28 

.7999  08  20 

.9057  71  16 

.9907  28  13 

23 

32 

48.8        11.2 

32 

38 

.0435  35  114 

.4549  51  44 

.6622  27  27 

.8019  28  20 

.9073  87  16 

.9919  40  13 

22 

28 

7  54.5  82  05.5  * 

36 

2  40 

44 

39 
40 
41 

.0548  48  111 

.4593  95  44 

.6650  54  27 

.8039  48  20 

.9089  03  16 

.9932  53  13 

21 
20 
19 

24 

1  20 

16 

8  00.2  81  59.8  *t 
05.8        54.2  f 
11.3        48.7  l* 

8.0658  58  109 

8.4637  38  43 

8.6677  82  27 

8.8059  67  20 

8.9104  18  16 

8.9945  66  13 

.0765  65  106 

.4680  82  43 

.6704  09  27 

.8078  87  20 

.9119  34  15 

.9958  79  13 

48, 

42 

.0870  70  103 

.4723  25  43 

.6731  36  27 

.8098  o7  20 

.9135  50  15 

.9970  92  13 

18 

12 

16.8       43.2  ll 

52^ 

43 

.0972  72  101 

.4765  67  42 

.6758  62  27 

.8117  26  19 

.9150  65  16 

.9983  05  13 

17 

08 

22.2        37.8  '" 

56 

300 

04 

44 
45 
46 

.1072  72    99 

.4807  09  42 

.6784  89  26 

.8137  46  19 

.9166  80  15 

8.9996  i7  13 

16 
15 
14 

04 

1  00 

56 

27.5        32.5  11 
32.8        27.2  j: 

38.1  21.9  J: 

43.2  16.8  :, 
48.4        11.6^; 

53.5    06.5  ■':: 

8  58.5  8101.5  l"; 

9  03.5  80  56.5  f  * 

08.4  51.6  ^^ 

13.3  46.7  „ 
18.2        41.8  " 
23.0        37.0  :° 
27.8       32.2  ^„ 

32.5  27.5  ^^ 
37.2        22.8  li 
41.8        18.2  " 

46.4  13.6  °^ 

9  51.0  8009.0  „* 
o       1    65 

8.1169  70    97 

8.4848  51  41 

8.6810  15  26 

8.8156  65  19 

8.9181  96  15 

9.0008  30  13 

.1265  65    94 

.4890  92  41 

.6837  42  26 

.8175  85  19 

.9196  11  16 

.0021  43  13 

08 

47 

.1358  59    92 

.4930  33  41 

.6863  68  26 

.8194  04  19 

.9211  26  16 

.0033  55  13 

13 

52 

12 

48 

.1450  50    90 

.4971  73  40 

.6889  94  26 

.8213  23  19 

.9226  41  16 

.0046  68  12 

12 

48 

16 

3  20 

24 

49 
50 
51 

.1539  40    89 

.5011  13  40 

.6914  20  26 

.8232  42  19 

.9241  56  15 

.0058  80  12 

11 

10 

09 

44 

0  40 

36 

8.1627  27    87 

8.5050  53  39 

8.6940  45  26 

8.8251  61  19 

8.9256  72  16 

9.0070  93  12 

.1713  13    85 

.5090  92  39 

.6965  71  25 

.8270  80  19 

.9271  87  16 

.0083  05  12 

28 

52 

.1797  98   84 

.5129  31  39 

.6991  96  25 

.8289  99  19 

.9286  02  18 

.0095  18  12 

08 

32 

32 

53 

.1880  80    82 

.5167  70  38 

.7016  21  26 

.8307  17  19 

.9301  16  16 

.0107  30  12 

07 

28 

36 

3  40 

44 

54 
55 

56 

.1961  62    80 

.5206  08  38 

.7041  46  25 

.8326  36  19 

.9315  31  15 

.0120  43  12 

06 
05 
04 

24 

0  20 

16 

8.2041  41    79 

8.5243  46  38 

8.7066  71  25 

8.8345  55  19 

8.9330  46  15 

9.0132  55  12 

.2119  20    78 

.5281  83  37 

.7090  96  25 

.8363  73  18 

.9345  61  16 

.0144  67  12 

48 

57 

.2196  96    76 

.5318  21  37 

.7115  21  25 

.8381  92  18 

.93.59  76  15 

.0156  80  12 

03 

12 

52 

58 

.2271  72    75 

.5355  58  37 

.7140  45  24 

.8400  10  18 

.9374  90  15 

.0168  92  12 

02 

08 

56 
4  00 

59 
60 

.2346  46    74 

.5392  94  37 

.7164  70  24 

.8418  28  18 

.9388  05  15 

.0180  04  12 

01 
00 

04 
000 

8.2419  19    72 

8.5428  31  36 

8.7188  94  24 

8.8436  46  18 

8.9403  20  14 

9.0192  16  12 

cos     ctn 

cos     ctn            cos     ctn            cos     ctn            cos     ctn            cos     ctn 

1 

m  a 

Angles.  0.00 

89°=  5"  56" 

8§o=  5'  52"  87°=  5"  48»  86°=  5''  44"  85°=  S"-  40»  84°=  S'  36" 

An 

SlM. 

CSC 

LOGARITHMIC    TRIGONOMETRIC    FUNCTIONS. 

65 

60 

55 

so 

1 

6.6 

6.8 

6.4 

6.3 

6.2        6 

.1 

5.0        8.9        5.8 

6.7        6.6        8.8         6.4        6.3         6.2 

6.1 

6.0        4.9 

4.8        4.7 

a 

13.2 

13.0 

12.8 

12.6 

12.4       12.2       12.0       11.8       11.6 

11.4      II.3      11.0      10.8      10.6      10.4 

10.2 

10.0         9.8 

9.6        9.4 

3 

19.8 

19.6 

19.2 

18.9 

18.6      18.3      18.0      17.7      17.4 

17.1       16.8       16.6       16.2       16.9       16.6 

15.3 

15.0       14.7 

14.4       U.I 

4 

26.4 

26.0 

25.6 

25.2 

24.8      24.4      24.0       23.6      23.2 

22.8       22.4      22.0      21.6      21.2      20.8 

20.4 

20.0       19.6 

19.2       18.8 

5 

33.0 

32.6 

32.0 

31.6 

31.0      30.5       30.0      29.6      29.0 

28.6      28.0      27.8      27.0      26.8      26.0 

28.8 

26.0      24.5 

24.0      23.5 

6 

39.6 

39.0 

38.4 

37.8 

37.2      36.6      36.0      35.4      34.8 

34.2      33.6      33.0      82.4       31.8       31.2 

30.6 

30.0      29.4 

28.8      28.2 

7 

46.2 

45.5 

44.8 

44.1 

43.4      42.7      42.0      41.3      40.6 

39.9       39.2      38.5       37.8       37.1       36.4 

35.7 

35.0      34.3 

33.6      32.9 

8 

62.8 

82.0 

61.2 

60.4 

49.6      48.8       48.0      47.3      46.4 

46.6      44.8      44.0      43.2       42.4      41.6 

40.8 

40.0      39.2 

J8.4       87.6 

9 

69.4 

68.6 

67.6 

56.7 

66.8       64.9      64.0      63.1       62.2 

61.3      60.4      49.8      48.6      47.7       46.8 

46.9 

45.0       44.1 

43.2       42.3 

98 

91 

i 

a 

0'  10'  20'  30'  40' 

50' 

60' 

(     m   8       J      m    a 

10  =  0  40    40  =  2  40 

20=120    50=320 

1 
2 
3 

9.8 
19.6 
29.4 

9.7 
19.4 
29.1 

9.6 
19.2 

28.8 

9.5 
19.0 

28.5 

9.4 
13.8 
28.2 

9.3 
18. G 
27.9 

9.2 
18.4 
27.6 

9.1 
18.2 
27.3 

a 

^ 

30  =  200    60=400 

5° 

sin 
tan 

8.9403  545  682 
8.9420  563  701 

816 
836 

945 
966 

o70 
o93 

9.  oi92 

9.  0216 

cos 
ctn 

s*"  36° 

4 

39.2 

38.8 

38.4 

38.0 

37.6 

37.2 

36.8 

36.4 

o""    20"" 

ctn 

1.0580  437  299 '164 

034 

907 

0.9784 

tan 

84° 

5 
6 

49.0 
88.8 

48.6 
68.2 

48.0 
67.6 

47.5 
67.0 

47.0 
66.4 

46.6 
66.8 

46.0 
65.2 

45.6 
64.6 

cos 
sin 

9.9983  982  981  980 

979 

977 

9.9976 

sin 
cos 

9.0192  311   426 

539 

648 

755 

9.0859 

7 

68.6 

67.9 

67.2 

66.6 

66.8 

65.1 

64.4 

63.7 

6° 

tan 

9.0216  336  453 

567 

678 

786 

9.0891 

ctn 

s""  32" 

8 

78.4 

71.6 

76.8 

76.0 

75.2 

74.4 

73.6 

72.8 

o"  24™ 

ctn 

0.9784   604  547 

433 

322 

214 

0.9109 

tan 

83° 

9 

88.3 

87.3 

86.4 

85.5 

84.6 

83.7 

82.8 

81.9 

cos 
sin 

9.9976  975  973  972 

971 

969 

9.9968 

sin 
cos 

s45 

9.  m36 

9.0859  961    o60 

ib7 

252 

90 

83 

7° 

tan 
ctn 

9.0891  995   o96 
0.9109  005   904 

i94 
806 

291 

709 

385 
cl5 

9.  h78 

0.8622 

ctn 
tan 

S""  28™ 
82° 

1 

9.0 
18.0 
27.0 

8.4 
16.8 
25.2 

2 
3 

17.8 
26.7 

17.6 
26.4 

17.4 
26.) 

17.2 
26.8 

17.0 
25.8 

16.6 
24.9 

cos 
sin 

9.9968  966  964 

963 

961 

959 

9.9958 

sin 
cos 

9.1436  525  612 

697 

781 

863 

9.1943 

4 
5 
6 

36.0 
49.0 
64.0 

35.6 
44.8 
63.4 

36.2 
44.0 
62.8 

34.8 
43.8 
62.2 

34.4 
43.0 
61. Q 

34.0 
42.6 
51.0 

33.6 
42.0 
60.4 

33.2 
41.5 
49.8 

8° 
qI^  32- 

tan 
ctn 
cos 

sin 

9.1478  569  658 
0.8522  431   342 
9.9958  956  954 

745 
255 
952 

831 
169 
950 

915 

085 
948 

9.1997 
0.8003 
9.9946 

ctn 
tan 
sin 

cos 

5"  24" 
81° 

9.1943    o22    lOO 

i76 

251 

.•!24 

9.  2S97 

7 

63.0 

62.3 

61.6 

60.9 

60.2 

59.6 

68.8 

.58.1 

r 

tan 

9.1997    o78    i58 

236 

3l3 

389 

9.  2463 

ctn 

5"  20" 
80° 

8 

72.0 

71.2 

70.4 

69.6 

68.8 

68.0 

67.2 

66.4 

o""  36™ 

ctn 

0.8003    922    842 

764 

g87 

611 

0.   7537 

tan 

9 

81.0 

80.1 

79.2 

78.3 

77.4 

76.6 

75.6 

74.7 

cos 
sin 

9.9946  944   942 

940 

938 

936 

9.9934 

sin 
cos 

9.2397  468  538  606  674 

740 

9.2806 

83 

75 

10° 

o*"  40" 

tan 

9.2463  536  609 

680  ''-'^ 

819 

9.2887 

ctn 

5"  16" 
79° 

1 

8.2 

8.1 

8.0 

7.9 

7.8 

7.7 

7.6 

7.6 

ctn 

0.7537  464   391 

320 

250 

181 

0.7113 

tan 

2 
3 

16.4 
24.6 

16.2 
24.3 

16.0 
24.0 

15.8 
23.7 

15.6 
23.4 

16.4 
23.1 

15.2 
22.8 

15.0 
22.5 

cos 
sin 

9.9934  931  929 

927 

924 

922 

9.9919 

sin 
cos 

9.2806  870  934 

997 

o58 

il9 

9.  3l79 

4 

32.8 

32.4 

32.0 

31.6 

31.2 

30.8 

30.4 

30.0 

11° 

tan 

9.2887  953    o20 

o85 

i49 

2l2 

9.  3275 

ctn 

5"  12" 

5 

41.0 

40.5 

40.0 

39.6 

39.0 

38.5 

38.0 

37.6 

0"  44" 

ctn 

0.7113  047    980 

9l5 

851 

788 

0.6725 

tan 

78° 

6 

7 
8 
9 

49.2 

87.4 
65.6 
73.8 

48.6 

66.7 
64.8 
72.9 

48.0 

66.0 
64.0 
72.0 

47.4 

65.3 
63.2 
71.1 

46.8 

64.6 
62.4 
70.2 

46.2 

63.9 
61.6 
69.3 

45.6 

83.2 
60.8 
68.4 

45.0 

62.5 
60.0 
67.5 

12° 

0"  48" 

13° 

0"  52-" 

cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 

9.9919  917  914 

912 

909 

907 

9.9904 

sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 

5''  oS" 
77° 

S*"  04"" 
76° 

9.3179  238  296 
9.3275  336  397 
0.6725  664  603 
9.9904  901   899 

353 

458 
542 
896 

410 
517 
483 
893 

466 
576 
424 
890 

9.3521 
9.3634 
0.6366 
9.9887 

r* 

er 

9.3521   575  629 
9.3634  091   748 
0.6366  309  252 

9.9887  884  881 

682 
804 
196 

878 

734 
859 
141 

875 

786 
914 
086 

872 

9.3837 
9.3908 
0.6032 
9.9869 

1 
2 
3 

7.4 
14.8 
22.2 

7.3 
14.6 
21.9 

7.3 
14.4 
21.6 

7.1 
14.2 
21.3 

7.0 
14.0 
21.0 

6.9 
13.8 

20.7 

6.8 
13.6 
20.4 

6.7 
13.4 
20.1 

9.3837  887  937 

986 

o35 

o83 

9.  4l30 

4 

29.6 

29.2 

28.8 

28.4 

28.0 

27.6 

27.2 

26.8 

14° 

tan 

9.3968    o2l    o74 

i27 

i78 

230 

9.  4281 

ctn 

K^   00" 

a 

37.0 

36.5 

36.0 

36.5 

35.0 

34.5 

34.0 

33.5 

0"  56-" 

ctn 

0.6032    979    926 

873 

822 

770 

0.  «7l9 

tan 

75° 

6 

7 
8 

44.4 

61.8 
69.3 

43.8 

61.1 
68.4 

43.2 

80.4 
67.6 

42.6 

49.7 
66.8 

42.0 

49.0 
66.0 

41.4 

48.3 
68.2 

40.8 

47.6 
64.4 

40.2 

46.9 
53.6 

cos 

9.9869  866  863  859 

856 

853 

9.9849 

sin 

i"=i5'    a 

2°=30'     4 

"=45' 
»=60' 

60'  50'  40'  30'  20' 

10' 

0' 

1 

9 

66.6 

65.7 

64.8 

63.9 

63,0 

62.1 

61.2 

60.3 

l'=0'.i 

!6 

LOGARITHMIC 

TRIGONOMETRIC    FUNCTIONS. 

43 

40 

33 

30 

1 

3 

3 

4 
5 
6 

7 
8 
9 

4.6 
9.3 
13.8 

18.4 
33.0 
27.6 

32.2 
36.8 
41.4 

4.5 
9.0 
13 .4 

18.0 
22.5 
27.0 

31.5 

36.0 
40.5 

4.4        4.3        4.2        4.1         4.0        3.9         3.8 
8.8        8.6        8.4        8.2        8.0        7.8         7.6 

13.2  12.9       12.6       12.3       12.0       11.7       11.4 

17.6       17.3       16.8       16.4       16.0       15.6       15.2 
22.0       21.5      21.0      20.5      20.0       19.5       19.0 
26.4      26.8      36.2      24.6      24.0      23.4      23.8 

30.8      30.1       39.4      38.7      28.0      27.3       36.6 

35.3  34.4      33.6      33.8       33.0      31.2       30.4 
.39.6       38.7      37.8       36.9       36.0      35.1       34.3 

3.7        3.6        3.5        3.4        3.3         3.2 
7.4        7.2        7.0        6.8        6.6        6.4 
11.1       10.8       10.5       10.2        9.9         9.6 

14.8  14.4       14.0       13.6       13.2       13.8 
18.6       18.0       17.5       17.0       16.6       16.0 
33.3      21.6      21.0      30.4       19.8       19.2 

25.9  35.3      34.6      33.8      23.1      32.4 
29.6      38.8      28.0      27.2      26.4      26.6 
83.3      82.4      31.6       30.6      29.7       28.8 

3.1  3.0 

6.2  6.0 

9.3  9.0 

12.4       12.0 
15.6       U'.O 

18.6  18.0 

31.7  21.0 

24.8  34.0 

27.9  27.0 

2.9        2.8        2.7 
5.8        6.6        6.4 
8.7        8.4        8.1 

11.6      11.3      10.8 
14.5       14.0       13.5 
17.4       16.8       16.2 

20.3       19.6       18.9 
23.2      22.4      21.6 
26.1       25.2      24.3 

130 

133 

•< 

i5 

0'  10'  20'  30'  40' 

50'  60' 

/     m   8       *      m    8 
10  =  0  40     40  =  2  40 

20=120    60=320 

30  =  200    60=400 

1 
2 
3 

4 
5 
6 

7 
8 
9 

13.0 
36.0 
39.0 

63.0 
65.0 
78.0 

91.0 
104.0 
117.0 

12.9 
35.8 
38.7 

51.6 
64.5 

77.4 

90.3 
103.2 
116.1 

13.8      12.7 
35.6     35.4 
38.4     38.1 

61.2     60.8 
64.0     63.5 
76.8     76.3 

89.6     88.9 
102.4    101.6 
115.2    114.3 

12.6 
36.3 
37.8 

60.4 
63.0 
75.6 

88.2 
100.8 
113.4 

12.6 
36.0 
37.6 

50.0 
63.5 
76.0 

87.5 
100.0 
112.5 

12.4 
34.8 
37.3 

49.6 
62.0 
74.4 

88.8 
99.2 
111.6 

12.3 
34.6 
36.9 

49.2 
61.6 
73.8 

86.1 
98.4 
110.7 

15° 

1^  oo"' 

16° 

i"*  04'" 

17° 

ih    08™ 

18° 
19° 

20° 

l""    20"" 

21° 

!■»    24™ 

22' 
23° 

24° 

i"  36™ 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 
sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

sin 
tan 
ctn 
cos 

9.4130   177  223 
9.4281  331  381 
0.5719  669  619 
9.9849  846  843 

269 
430 
570 
839 

314 
479 
521 
836 

359  9.4403 
527  9.4575 
473  0.5425 
832  9.9828 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

cos 
ctn 
tan 
sin 

4*'  56" 

74° 

4"  52" 
73° 

4"  48" 
72° 

4"  44" 
71° 

4*  40" 
70° 

69° 

4"  32" 
68° 

4'"  28"- 
67° 

4''  24" 
66° 

4''  20" 
65° 

9.4403  447  491 
9.4575  622  669 
0.5425  378  331 

9.9828  825  821 

533 
716 

284 
817 

576 
762 
238 

814 

618  9.4659 
808  9.4853 
192  0.5147 
810  9.9806 

9.4659  700  741 
9.4853  898  943 
0.5147  102  057 
9.9806  802  798 

781 
987 
013 
794 

821 
o31 
869 
790 

861   9.4900 
o75    9.  5il8 
925   0.  4882 
786  9.9782 

133 

115 

1 
2 
3 

4 
5 
6 

7 
8 
9 

12.2 
34.4 
36.6 

48.8 
61.0 
73.3 

85.4 
97.6 
109.8 

12.1 
34.2 
36.3 

48.4 
60.5 
73.6 

81.7 
96.8 
108.9 

12.0      11.9 
34.0     23.8 
36.0     35.7 

48.0     47.6 
60.0     69.6 
72.0     71.4 

84.0     83.3 
96.0     95.2 
108.0    107.1 

11.8 
23.6 
36.4 

47.2 
59.0 
70.8 

82.6 
94.4 
106.3 

11.7 
33.4 
35.1 

46.8 
68.6 
70.2 

81.9 
93.6 
105.3 

11.6 
23.2 
34.8 

46.4 
58.0 
69.6 

81.2 
92.8 
104.4 

11.5 
23.0 
34.6 

46.0 
67.5 
69.0 

80.5 
92.0 
103.5 

9.4900  939  977 
9.5118  161  203 
0.4882  839  797 
9.9782  778  774 

ol5 
245 
755 
770 

o52 
287 
713 
765 

o90    9.  5i26 
329  9.5370 
671  0.4630 
761   9.9757 

9.5126  1G3  199 
9.5370  411  451 
0.4630  589  549 
9.9757  752  748 

235 
491 
509 
743 

270 
531 
469 
739 

306  9.5341 
571   9.5611 
429  0.4389 
734  9.9730 

114 

lor 

9.5341   375  409 
9.5611  650  689 
0.4389  350  311 
9.9730  725  721 

443 

727 
273 
716 

477 
766 
234 
711 

510  9.5543 
804  9.5842 
196  0.4158 
706  9.9702 

1 
2 
3 

4 
5 
6 

7 
8 
9 

.1.4 

22.8 
34.2 

45.6 
57.0 
68.4 

79.8 
91.2 
102.6 

11.3 
22.6 
33.9 

45.2 
56.5 
67.8 

79.1 
90.4 
101.7 

11.3  11.1 

32.4  22.2 
33.6     33.3 

44.8     44.4 
56.0     55.5 
67.2     66.6 

78.4     17.7 
89.6     88.8 
100.8     99.9 

11.0 

22.0 
33.0 

44.0 
55.0 
66.0 

77.0 
88.0 
99.0 

10.9 

21.8 
32.7 

43.6 
54.6 
65.4 

76.8 
87.3 
98.1 

10.8 
21.6 
32.4 

43.3 
54.0 
64.8 

75.6 
86.4 
97.2 

10.7 
21.4 
32.1 

42.8 
63.5 
64.2 

74.9 
86.6 
96.3 

9.5543  576  609 
9.5842  879  917 
0.4158  121  083 
9.9702  697  692 

641 
954 
046 

687 

673 
991 
009 
682 

704  9.5730 
o28    9.0064 
972    0.  3936 
677  9.9672 

9.5736  767  798 
9.6064   100  136 
0.3936  900  864 
9.9672  667  661 

828 
172 
828 
656 

859 
208 
792 
651 

889  9.5919 
243  9.6279 
757  0.3721 
646  9.9640 

106 

»9 

9.5919  948  978 
9.0279  314  348 
0.3721   686  652 
9.9640  635  629 

o07 
383 
617 
624 

o36 
417 
583 

618 

o65    9.  6093 
452  9.6486 
548  0.3514 
613  9.9607 

1 
2 
3 

4 
5 
6 

7 
8 
9 

10.6 
21.2 
31.8 

43.4 
53.0 
63.6 

74.9 
84.8 
95.4 

10.5 
31.0 
31.5 

43.0 
52.5 
63.0 

73.5 
84.0 
94.5 

10.4      lO.S 
30.8     20.6 

31.3  30.9 

41.6     41.3 
53.0     51.5 

62.4  61.8 

72.8     72.1 
83.2     82.4 
93.6     92.7 

10.3 
30.4 
30.6 

40.8 
61.0 
61.2 

71.4 
81.6 
91.8 

10.1 
20.2 
30.3 

40.4 
60.5 
60  .< 

70.7 
80.8 
90.9 

10.0 
30.0 
30.0 

40.0 
50.0 
60.0 

70.0 
80.0 
90.0 

9.9 
19.8 
29.7 

39.6 
49.6 
69.4 

69,3 
79.2 
89.1 

9.6093   121   149 
9.6486  520  553 
0.3514  480  447 
9.9607  602  596 

177 
587 
413 
590 

205 
620 
380 

584 

232  9.6259 
654  9.6687 
346  0.3313 
579  9.9573 

1-=15'      3 

2»=30'     4 

l'=0'.J 

°  =  4.V 
!5 

60'  50'  40'  30'  20' 

10'  0' 

Bi 

>• 

r 

LOGABITHMIC    TRIGONOMETRIC 

FUNCTIONS 

, 

Angles  in  All 

QUADKANTS. 

Names. 

-qp        0°         qi        so°—<p    »0°    no°+<)p    180°-()P  180= 

i3o°+qp  27o°-qp  aro° 

270°+qp 

360°- 

JP  360°  360°+qp 

sin 

-sin  ip   '■ 

FO 

+8in  9  +C0S  (jp 

+  1 

+COS  qp  +sin  qp 

±0 

—sin  qp  —cos  qp 

-1 

-COS  qp 

-sin 

<iP 

TO 

+sin  qp 

COS 

CSC 

-CSC  cp    - 

poo 

+CSC  qp  +sec  (f) 

+  1 

+sec  qp  +CSC  qp 

±oc 

—CSC  qp  —sec  qp 

-1 

-sec  qp 

-CSC 

9> 

Tod 

+CSC  <fi 

sec 

tan 

-tan  (p  = 

FO 

+tan  (f  +ctn  qp 

±QC 

-Ctn  qp  -tan  qp 

TO 

+tan  qp  +ctn  qp 

±00 

-Ctnqp 

-tan 

<P 

TO 

+tanqp 

ctn 

ctn 

-ctn  (f  - 

F<x 

+ctn  qp  +tan  qp 

±0 

-tan  qp  -Ctn  qp 

Too 

+ctn  qp  +tan  qp 

±0 

-tanqp 

-ctn 

9 

TOO 

+Ctnqp 

tan 

sec 

+sec()B  - 

Kl 

+sec  qp  +CSC  qp 

±00 

-CSC  qp  -sec  qp 

-1 

-sec  qp  -CSC  qp 

TOO 

+CSCqp 

+sec 

<f 

+  1 

+secqp 

CSC 

cos 

+COS  (jp    - 

H 

+COS  qp  +sm  qp 

±0 

— sm  qp  -COS  qp 

-1 

-COS  qp  -sin  qp 

TO 

+sin  qp 

+COS 

9P 

+  1 

+COSqp 

sin 

810°+qp  810"  810°-g)  720°+(p    TSO"  720°-q)   630°+()B  630 

'  630°-qp   540° +qp 

S40< 

840°-qp 

450°+qP  450°  460 

»-qp 

Names. 

Angles  in  All 

Quadrants. 

1 

•< 

1 

0'  10'  20'  30'  40'  50'  60' 

'    m   8       '      ni    8 
10=0  40    40=2  40 

20=120    60=320 

30  =  200    60=400 

Proportional  Parts. 

1 

3 

3       4 

5 

6      y 

8 

9 

sin 

9.6259  286  313 

340 

366  392  9.6418 

COS 

2.6 

5.3 

7.9 

10.6 

13.2 

16.9 

18.6 

21,2 

23.8 

25° 

i''  40" 

tan 
Ctn 

9.6687  720  752 
0.3313  280  248 

785 
215 

817  850  9.6882 
183  150  0.3118 

Ctn 
tan 

4"  16" 
64° 

3.3 

3.6 

9.8 

13.0 

16.3 

19.6 

22.8 

26.0 

29.3 

cos 

sin 

9.9573  567  561 

555 

549  543  9.9537 

sin 
cos 

0.6 

1.2 

1.8 

2.4 

3,0 

3.6 

4.2 

4.8 

5,4 

9.6418  444  470 

495 

521  546  9.6570 

2.5 

).l 

7.6 

10.1 

12.7 

15.2 

17.7 

20.3 

22,8 

26° 

I*"  44" 

tan 
Ctn 

9.6882  914  946 
0.3118  086  054 

977 
023 

o09    o40    9.  7o72 

991     960     0.  2928 

Ctn 

tan 

4''  12" 
63° 

3.2    6.3 

9.6 

12.7 

16.8 

19.0 

22.1 

26.3 

28,6 

COS 

sin 

9.9537  530  524 

518 

512  505  9.9499 

sin 
cos 

0.6 

.3 

1.9 

2.5 

3.1 

3.8 

4.4 

6.0 

5.7 

9.6570  595  620 

644 

668  692  9.6716 

2.4    4.9 

7.3 

9.7 

12.1 

14.6 

17,0 

19.4 

21.8 

21° 

i"  48"" 

tan 
ctn 

9.7072  103  134 
0.2928  897  866 

165 
835 

196  226  9.7257 
804  774  0.2743 

ctn 
tan 

4"  08"" 
62° 

3.1    6.2 

9.3 

12.3 

16.4 

18.6 

21.6 

24.7 

27.8 

cos 
sin 

9.9499  492  486 

479 

473  466  9.9459 

sin 
cos 

0.7 

.3 

2.0 

2.6 

3.3 

3.9 

4.6 

6.3 

5,9 

9.6716  740  763 

787 

810  833  9.6856 

2.3       4.7 

7.0 

9.3 

11.6 

14.0 

16.3 

18.6 

20.9 

28° 
1^  52" 

tan 
ctn 

9.7257  287  317 
0.2743  713  683 

348 
652 

378  408  9.7438 
622  592  0.2562 

ctn 
tan 

4*"  04" 
61° 

3.0       6.0 

9.0 

12.1 

15.1 

18.1 

21.1 

24.1 

27.1 

cos 
sin 

9.9459  453  446 

439 

432  425  9.9418 

sin 
cos 

0.7 

.4 

2,1 

2.7 

3.4 

4.1 

4.8 

6.6 

6.2 

9.6856  878  901 

923 

946  968  9.6990 

2.2       4.5 

6.7 

8.9 

11.2 

13.4 

16,6 

17.9 

20.1 

29° 

tan 
ctn 

9.7438  467  497 
0.2562  533  503 

526 
474 

556  585  9.7614 
444  415  0.2386 

ctn 
tan 

4''  00" 
60° 

2,9       6.9 

8.8 

11.8 

14.7 

17.7 

20.6 

23.6 

26.5 

cos 
sin 

9.9418  411  404 

397 

390  383  9.9375 

sin 
cos 

0.7 

.4 

2,1 

2.9 

3.6 

4.3 

6.0 

6.7 

6.4 

9.6990    ol2    o33 

o55 

o76   o97    9.  nl8 

2.1       4.3 

6.4 

8.6 

10.7 

12.9 

15,0 

17.2 

19.3 

30° 

2^  00" 

tan 
ctn 

9.7614  644  673 
0.2386  356  327 

701 
299 

730  759  9.7788 
270  241  0.2212 

ctn 
tan 

59° 

2.9       5.8 

8.7 

11.6 

14.4 

17.3 

20.2 

23.1 

26.0 

cos 
sin 

9.9375  368  361 

353 

346  338  9.9331 

sin 
cos 

0.7 

.5 

2.2 

3.0 

3.7 

4,5 

5.2 

6.0 

6.7 

9.7118  139  160 

181 

201  222  9.7242 

2.1       4.1 

6.2 

8.2 

10.3 

12.4 

14.4 

16.6 

18.6 

31° 

2"  04° 

tan 

ctn 

9.7788  816  845 
0.2212  184  155 

873 
127 

902  930  9.7958 
098  070  0.2042 

ctn 
tan 

3''  52- 
58° 

2.8       6.7 

8.5 

11.3 

14.2 

17.0 

19.9 

22.7 

26.6 

cos 

sin 

9.9331  323  315 

308 

300  292  9.9284 

sin 
cos 

0.8 

.6 

2.3 

3.1 

3.9 

4.6 

5.4 

6,2 

7.0 

9.7242  262  282 

302 

322  342  9.7361 

2.0       4.0 

6.9 

7.9 

9,9 

11.9 

13.9 

15,9 

17.8 

32° 

2"  08" 

tan 
ctn 

9.7958  986    ol4 
0.2042  014    986 

o42 

958 

o70    o97   9.  8i25 
930    903   0.  1875 

ctn 
tan 

3"  48«' 
57° 

2.8       6.6 

8.4 

11.2 

13.9 

16.7 

19.5 

22.3 

25.1 

cos 
sin 

9.9284  276  268 

260 

252  244  9.9236 

sin 
cos 

0.8        1.6 

2,4 

3.2 

4,0 

4.8 

5,6 

6.4 

7.2 

9.7361   380  400 

419 

438  457  9.7476 

1.9       3.8 

5.7 

7.6 

9.6 

11.6 

13,4 

15.3 

17.2 

33° 

2"  12" 

tan 
ctn 

9.8125  153  180 
0.1875  847  820 

208 
792 

235  263  9.8290 
765  737  0.1710 

ctn 
tan 

S*"  44" 
56° 

2.7       6.5 

8.2 

11.0 

13.7 

16.5 

19.2 

22.0 

24.7 

cos 

sin 

9.9236  228  219  211 

203  194  9.9186 

sin 
cos 

0.8       1.7 

2.5 

3.3 

4,2 

6,0 

5.9 

6.7 

7.6 

9.7476  494  513 

531 

550  568  9.7586 

1.8       3.7 

5,5 

7.4 

9.2 

11,0 

12.9 

14.7 

16.6 

34° 

2"  16" 

tan 

ctn 

9.8290  317  344 
0.1710  683  656 

371 
629 

398  425  9.8452 
602  575  0.1548 

ctn 
tan 

t  40" 
55° 

2.7       6.4 

8.1 

10.8 

13.6 

16.2 

18.9 

21.7 

24.4 

cos 

9.9186  177  169 

160 

151  142  9.9134 

sin 

0.9 

.7 

2.6 

3.5 

4.3 

6.2 

6.1 

6,9 

7.8 
9 

1°=15'      3°=46' 

a 
p 

> 

D 
t 

1 

3 

3       4 

3 

6         7 

8 

2"=3C 
1' 

I"    4 

=0'. 

25 

60'  50'  40' 

m 

20'  10'  0' 

^ 

Proportional  Parts. 

10 


r 


LOGARITH  mC    TRIGONOMETRIC 

FUNCTIONS. 

Points  of  tue  Compass. 

Namoi. 

sin 

Oi 

3J      OJ       1       li      n       IJ 

2         2i        2i        2} 

3 

3i 

3J 

3i        4 

8.6908    8.9913    9.16e5    9.390-2 

9.3856    9.4628    9.6275    9.5828 

9.6310    9.6734    9.7110 

9.7447 

9.7750 

9.8024 

9.8271    9.8495 

cos 

CSC 

1.3092    1.0087    0.8335    0.7098 

0.6144    0.5372    0.4725    0.4172 

0.3690    0.3366    0.289C 

0.3553 

0.3350 

0.1976 

0.1729    0.1505 

sec 

tan 

8.6913    8.9934    9.1712    9.3987 

9.3988    9.4819    9.5536    9.6173 

9.6748    9.7280    9.7777 

9.8349 

9.8702 

9.9142 

9.9573    0.0000 

etn 

etn 

1.3087    1.0066    0.8388   0.7013 

0.6013    0.6181    0.4464    0.3828 

0.3252    0.2720    0.3233 

0.1751 

0.1298 

0.0858 

0.0427    0.0000 

tan 

sec 

0.0005    0.0021    0.0047    0.0084 

0.0132    0.0191    0.0263    0.0344 

0.0438    0.0546    0.0667 

0.0803 

0.0952 

0.1118 

0.1302    0.1505 

CSC 

cos 

9.9995    9.9979    9.99S3    9.9916 

9.9868    9.9809    9.9738    9.9656 

9.9562    9,9454    9.9333 

9.9198 

9.9048 

9.8883 

9.8698    9.8495 

sm 

7* 

ri       7i        7       tii       6i       6i 

6         5i        5.i        5i 

5 

4J 

4i 

4i        4 

Names. 

Points  of  the  Compass. 

3 

t 

0'  IC  20'  30'  40'  50'  60' 

'     m  8       '     m   8 
10=0  40    40=2  40 

20=120    50=3  20 

Proportional  Parts. 

si 

30=2  00    60=4  00 

1 

» 

3       4 

5 

«        7 

8 

• 

sin 

9.7586  604  622 

640 

657  675  9.7692 

cos 

1.8 

3.6 

6.3 

7.1 

8.9 

10.6 

12.4 

14.2      15.9 

35° 

2''  20-" 

tan 
etn 

9.8452  479  506 
0.1548  521  494 

533 
467 

559  586  9.8613 
441  414  0.1387 

etn 
tan 

3"  36" 
54° 

3.7 

6.3 

8.0 

10.7 

13.4 

16.0 

18.7 

21.4     24.1 

cos 
sin 

9.9134   125  116 

107 

098  089  9.9080 

sm 

cos 

0.9 

1.8 

2.7 

3.6 

4.5 

6.4 

6.3 

7.2        8.1 

9.7692  710  727 

744 

761  778  9.7795 

1.7 

3.4 

6.1 

6.8 

8.5 

10.2 

12.0 

13.7      15.4 

36° 

2"  24"" 

tan 
etn 

9.8613  639  666 
0.1387  361  334 

692 
308 

718  745  9.8771 
282  255  0.1229 

etn 
tan 

3"  32" 
53° 

2.6 

6.3 

7.9 

10.6 

13.2 

15.9 

18.6 

21. 

1      33.8 

cos 
sin 

9.9080  070  061 

052 

042  033  9.9023 

sm 
cos 

0.9 

1.9 

2.8 

3.7 

4.7 

6.6  ]     6.5 

7.5        8.4 

9.7795  811  828 

844 

861  877  9.7893 

1.6 

3.3 

4.9 

6.6 

8.2 

9.9 

11.6 

13.2      14.8 

37° 

2"  28"- 

tan 
etn 

9.8771  797  824 
0.1229  203  176 

850 
150 

876  902  9.8928 
124  098  0.1072 

etn 
tan 

3"  28" 
52° 

3.6 

6.2 

7.8 

10.6 

13.1 

15.7 

18.3 

20.9     23.5 

cos 
sin 

9.9023  014  004 

895 

985   o75    9.  8065 

sin 
cos 

I.O 

1.9 

3.9 

3.9 

4.8 

5.8 

6.8 

7.8       8.7 

9.7893  910  926 

941 

957  973  9.7989 

1.6 

3.3 

4.8 

6.4 

7.9 

9.5 

11.1 

12.7      14.3 

38° 
2''  32™ 

tan 
etn 

9.8928  954  980 
0.1072  046  020 

a06 
994 

o32   o58    9.  9084 
!)68    942    0.0016 

etn 
tan 

3"  24" 
51° 

3.6 

6.3 

7.8 

10.4 

13.0 

15.6 

18.2 

30.7     23.3 

cos 
sin 

9.8965  955  945 

935 

925  915  9.8905 

sm 
cos 

1.0 

2.0 

3.0 

4.0 

6.0 

6.0 

7.0 

8.0        9.0 

9.7989   o04    o20 

<^5 

o50   o66    9.  8o81 

1.5 

3.1 

4.6 

6.1 

7.7 

9.2 

10.7 

12.3      13.8 

39° 

2"  36" 

tan 
etn 

9.9084   110  135 
0.0916  890  865 

161 
339 

187  212  9.9238 
813  788  0.0762 

etn 

tan 

3'>  20" 
50° 

2.6 

6.1 

7.7 

10.3 

12.9 

15.4 

18.0 

20.6     23.2 

cos 
sin 

9.8905  895  884 

874 

864  853  9.8843 

sm 

cos 

1.0 

3.1 

3.1 

4.3 

5.2 

6.3 

7.3 

8.3       fl.4 

9.8081  096  111 

125 

140  155  9.8169 

1.0 

3.0 

4.4 

6.9 

7.4 

8.9 

10.4 

11.8      13.3 

40° 

2''  40"" 

tan 
etn 

9.9238  264  289 
0.0762  736  711 

315 

685 

341  366  9.9392 
659  634  0.0608 

etn 
tan 

3»  1 6-" 
49° 

2.6 

5.1 

7.7 

10.3 

12.8 

15.3 

17.9 

20.5      23.0 

cos 

sin 

9.8843  832  821 

810 

800  789  9.8778 

sin 
cos 

1.1 

2.2 

3.2 

4.3 

6.4 

6.5 

7.6 

8.6       9.7 

9.8169  184  198  213 

227  241   9.8255 

1.4 

2.9 

4.3 

5.7 

7.1 

8.6 

JO.O 

11.4      12.9 

41° 

2''  44" 

tan 
etn 

9.9392  417  443  468 
0.0608  583  557  532 

494  519  9.9544 
506  481  0.0456 

etn 
tan 

3"    I2» 

48° 

2.5 

6.1 

7.6 

10.2 

12.7 

15.3 

17.8 

20.4     22.9 

cos 
sin 

9.8778  767  756  745 

733  722  9.8711 

sin 
cos 

i.i 

2.2 

3.4 

4.5 

5.6 

6.7 

7.8 

8.9      10. 1 

9.8255  269  283 

297 

311   324  9.8338 

1.4 

2.8 

4.1 

5.5 

6.9 

8.3 

9.7 

11. 

D      12.4  II 

42° 

2'"  48"' 

tan 
etn 

9.9544  570  595 
0.0456  430  405 

621 
379 

646  671   9.9697 
354  329  0.0303 

etn 
tan 

3>'  o8"> 
47° 

2.3 

6.1 

7.6 

10.1 

12.7 

15.2 

17.8 

30.3      33.8 

cos 
sin 

9.8711  699  688 

676 

665  653  9.8641 

sm 
cos 

1.2 

3.3 

3.6 

4.6 

6.8 

6.9 

8.1 

9.3      10.4 

9.8338  351  365 

378 

391  405  9.8418 

1.3 

3.7 

4.0 

6.3 

6.7 

8.0 

9.3 

10.7      12.0 

43° 

tan 
etn 

9.9697  722  747 
0.0303  278  253 

772 
228 

798  823  9.9848 
202  177  0.0152 

etn 
tan 

3"  04'" 
46° 

2.5 

6.1 

7.6 

10.1 

12.7 

15.2 

17.7 

20.2     22.8 

cos 
sin 

9.8641  629  618  606 

594  582  9.8569 

sin 
cos 

1.3 

3.4 

3.6 

4.8 

6.0 

7.2 

8.4 

9.6      10.8 

9.8418  431  444 

457 

469  482  9.8495 

1.3 

2.6 

3.9 

5.1 

6.4 

7.7 

9.0 

10.3      11.6 

44° 

2"  56" 

tan 
etn 

9.9848  874  899 
0.0152  126  101 

924 

076 

949  975   0.  ooOO 
051  025  0.0000 

etn 
tan 

3"  00" 
45° 

2.8 

6.1 

7.6 

10.1 

13.6 

15.2 

17.7 

90.2     22.7 

cos 

9.8569  557  545  532 

520  507  9.8495 

sin 

1.3 

2.5 

3.7 

6.0 

6.2 

7.4 

8.7 

9.9     11.3 

f=W     8"=45' 

GA/      fan      J  A/      9AJ      a/\l      tAI      At 

Si 

t 

1 

» 

3       4 

9 

6         T 

S 

9 

2"=3(y     - 
1'= 

4 
=0'. 

-=60' 
25 

W   av  W 

«»w 

itV    IV    V 

' 

Proportional  Parts 

• 

11 


INVERSE    TRIGONOMETRIC 

FUNCTIONS. 

log^  sin"'^          cos"M    tati"^^ 

ctn-'^ 

s 

m 
+ 

3 

ii 

"cfi 

'11 

1) 

3 
C 

's 

_c 

8- 

o 

i 

V 

log^ 

sin"M       cos"'^ 

tair'^     ctn-M 

8.50 

.51 
.52 
.53 
.54 

8.55 
.56 
.57 

.58 
.59 

8.60 

.61 
.62 
.63 
.64 

8.65 
.66 
.67 
.68 
.69 

8.70 

.71 
.72 
.73 
.74 

8.75 

.76 
.77 

.78 
.79 

8.80 

.81 

.82 
.83 

.84 

8.85 

.86 
.87 
.88 
.89 

8.90 

.91 
.92 
.93 
.94 

8.95 

.96 
.97 

.98 
.99 

9.00 

O          /           t             o             * 

1  48.7   0.35    88  11.3 

0  1            t 

1  48.7   0.25 

o         r 

88  11.3 

1.50 

.49 

.48 
.47 
.46 

1.45 
.44 
.43 
.42 
.41 

1.40 

.39 
.38 
.37 
.36 

1.35 

.34 
.33 
.32 
.31 

1.30 

.29 

.28 
.27 
.26 

1.25 
.24 
.23 
.22 
.21 

1.20 

.19 
.18 
.17 
.16 

1.15 

.14 
.13 
.12 
.11 

1.10 

.09 

.08 
.07 
.06 

1.05 

.04 
.03 
.02 
.01 

1.00 

9.00 

.01 
.02 
.03 
.04 

9.05 

.06 
.07 
.08 
.09 

9.10 

.11 
.12 
.13 
.14 

9.15 

.16 
.17 

.18 
.19 

9.20 

.21 
.22 
.23 
.24 

9.25 

.26 
.27 

.28 
.29 

9.30 

.31 
.32 
.33 
.34 

9.35 

.36 
.37 
.38 
.39 

9.40 
.41 
.42 
.43 
.44 

9.45 

.46 
.47 

.48 
.49 

9.50 

Of/             O        i 

5  44    0.8    84  16 

o        /          / 

5  43    0.8 

0           f 

84  17 

1.00 

0.99 
.98 
.97 
.96 

0.95 
.94 
.93 
.92 
.91 

0.90 

.89 

.88 
.87 
.86 

0.85 

.84 
.83 
.82 
.81 

0.80 

.79 

.78 
.77 
.76 

0.75 
.74 
.73 
.72 
.71 

0.70 

.69 
.68 
.67 
.66 

0.65 
.64 
.63 
.62 
.61 

0.60 

.59 

.58 
.57 
.56 

0.55 

.54 
.53 
.52 
.51 

0.50 

1  51.3    0.26    88  08.7 
1  53.9   0.26    88  06.1 
1  56.5   0.27    88  03.5 
1   59.2    0  27    88  00.8 

1    51.2     0.26 

1  53.8   0.26 
1  56.4   0.27 
1  59.2   0.27 

88  08.8 
88  06.2 
88  03.6 
88  00.8 

5  52    0.8    84  08 

6  01    0.8   83  59 
6  09    0.9    83  51 
6  18    0.9    83  42 

5  51    0.8 

5  59   0.8 

6  07   0.8 
6  15   0.9 

84  09 
84  01 
83  .53 
83  45 

2  02.0    0.28    87  58.0 

2   01.9     0.28 

87  58.1 

6  27    0.9    83  33 

6  24   o.n 

83  30 

2  04.8    0.29    87  55.2 
2  07.8   0.29    87  52.2 
2  10.7   0.30    87  49.3 
2  13.8   0.31    87  46.2 

2  04.8   0.29 
2  07.7   0.29 
2  10.6   0.30 
2  13.7   0.31 

87  55.2 
87  52.3 
87  49.4 
87  46.3 

6  36    0.9    83  24 
6  45    0.9    83  15 

6  54    1.0    83  06 

7  04    1.0    82  56 

6  33   0.9 
6  42   0.9 

6  51    0.9 

7  01    1.0 

83  27 
83  18 
83  09 
82  59 

2  16.9   0.32    87  43.1 

2  16.8   0.31 

87  43.2 

7  14    1.0    82  46 

7  11    1.0 

82  49 

2  20.1   0.32    87  39.9 
2  23.4   0.33   87  36.6 
2  26.7   0.34    87  33.3 
2  30.1    0.35    87  29.9 

2  20.0   0.32 
2  23.2   0.33 
2  26.6   0.34 
2  30.0   0.34 

87  40.0 
87  36.8 
87  33.4 
87  30.0 

7  24    1.0    62  36 
7  35    1.1    82  25 
7  45    1.1    82  15 
7  56    11    82  04 

7  20    1.0 
7  31    i.o 
7  41    1.0 
7  52    1.1 

82  40 
82  29 
82  19 
82  08 

2  33.6   oM    87  26.4 

2  33.5   0.35 

87  26.5 

8  07    1.1    81  53 

8  02    1.1 

81  58 

2  37.2   0.36    87  22.8 
2  40.9   0.37    87  19.1 
2  44.6   0.38    87  15.4 
2  48.4    0.39    87  11.6 

2  37.0   0.36 
2  40.7   0.37 
2  44.4   0.38 
2  48.2   0.39 

87  23.0 
87  19.3 
87  15.6 
87  11.8 

8  19    1.2    81  41 
8  30    1.2    81  30 
8  42    1.2   81  18 
8  55    1  2    81  05 

8  13    1.1 
8  25   1.1 
8  36    1.2 

8  48    12 

81  47 
81  35 
81  24 
81  12 

2  52.4    0.40    87  07.6 

2  52.2   n.40 

87  07.8 

9  07    1.:)    80  53 

9  00    12 

81  00 

2  56.4    0.41    87  03.6 

3  00.5   0.42   86  59.5 
3  04.7   0.43   86  55.3 
3  09.0   0.44    86  51.0 

2  56.2   0.40 

3  00.3   0.41 
3  04.4   0.42 
3  08.7   0.43 

87  03.8 
86  .59.7 
86  55.6 
86  51.3 

9  20    1.3    80  40 

9  33    1.3    80  27 

9  47    1.4    80  13 

10  00    1.4    80  00 

9  13    1.3 
9  25    1.3 

9  38    1.3 
9  52    13 

80  47 
80  35" 
80  22 

80  08 

3  13.4   0.4.5    86  46.6 

3    13.1     0.44 

86  46.9 

10  15    1.4    79  45 

10  05    14 

79  55 

3  17.9   0.46    86  42.1 
3  22.5   0.47    86  37.5 
3  27.3   0.48   86  32.7 
3  32.1    0.49    86  27.9 

3  17.6    0.45 
3  22.2   0.46 
3  36.9   0.48 

3   31.7    0.49 

86  42.4 
86  37.8 
86  33.1 
86  28.3 

10  2<)    1.6    79  31 
10  44    1,5    79  16 

10  59    1.5    79  01 

11  15    1.6    78  45 

10  19    1.4 
10  33    1.4 

10  47    1.6 

11  02    1  5 

79  41 
79  27 
79  13 

78  58 

3  37.1    0.50    86  22.9 

3  36.6   0.50 

86  23.4 

11  31     1.6    78  29 

11     17      15 

78  43 

3  42.1    0.51    86  17.9 
3  47.3   0.52    86  12.7 
3  52.6   0.54    86  07.4 
3  58.0   0.O-,    86  02.0 

3  41.7   0.51 
3  46.8   0.62 

3  52.1     0.53 

3  57.5   0.55 

86  18.3 
86  13.2 
86  07.9 
86  02.5 

11  47    1.7    78  13 

12  04    1.7    77  56 
12  21    1.7    77  39 
12  38    1.8    77  22 

11  32    1.6 

11  48    1.6 

12  04    1.6 
12  20    1.7 

78  28 
78  12 
77  56 
77  40 

4  03.6    0.56    85  56.4 

4  03.0   0.56 

85  57.0 

12  56    1.8    77  04 

12  37    17 

77  23 

4  09.3   0.57    85  50.7 
4  15.1    0.59    85  44.9 
4  21.0   0.60    85  39.0 
4  27.1    0.62    85  32.9 

4  08.6   0.67 
4  14.4    0.58 
4  20.3   0.60 
4  26.3   0.61 

85  51.4 
85  45.6 
85  39.7 
85  33.7 

13  15    1.9    76  45 
13  33    1.9    76  27 

13  53    2.0    76  07 

14  13    2.0    75  47 

12  54    1.7 

13  12    1.8 
13  29    1.8 

13  48    1.8 

77  00 
76  48 
70  31 
76  12 

4  33.4    0.63    85  26.6 

4  32.5   0  62 

85  27.5 

14  33    2.1    75  27 

14  06    19 

75  54 

4  39.7   0.65    85  20.3 
4  46.3   0.66    85  13.7 
4  53.0   0.68    85  07.0 
4  59.8   0.69    85  00.2 

4  38.8   0.64 
4  45.3   0.65 
4  51.9   0.67 
4  58.7   0.68 

85  21.2 
85  14.7 
85  08.1 
85  01.3 

14  54    2.1    75  00 

15  15    2.2    74  45 
15  37    2.2    74  23 
15  59    2.3    74  01 

14  25    1.9 

14  44    1.9 

15  04    2.0 
15  24    2.0 

75  35 
75  16 
74  56 
74  30 

5  06.8   0.71    84  53.2 

5  05.6   0.70 

84  54.4 

16  22    2.3    73  38 

15  44    2.1 

74  16 

5  14.0   0.72    84  46.0 
5  21.3   0.74   84  38.7 
5  28.8   0.76    84  31.2 
5  36.5   0.78    84  23.5 

5   12.7    0.72 

5  19.9   0.73 
5  27.3   0.75 
5  34.9   0.77 

84  47.3 
84  40.1 
84  32.7 
84  25.1 

16  46    2.4    73  14 

17  10    2.4    72  50 

17  35    2.5    72  25 

18  00   i.6    72  00 

10  05   2.1 
16  27   2.1 

16  48   2.2 

17  10     2.2 

73  55 
73  33 
73  12 
72  50 

5  44.4    0.80    84  15.6 

off           Of 

5  42.6   0.78 

0         '         / 

84  17.4 

O          1 

18  26    a.6    71  34 

off         of 

17  33   2.3 

o      f        f 

72  27 
o      ' 

CSC" '.4          sec'M     ctn"M 

tan-'^ 

log -4 

csc'^        sec' 'J 

ctn-M 

tan"M  log^ 

12 


INVERSE    TRIGONOMETBIC 

FUNCTIONS. 

log  ^  sin"  M        cos"'^  tan'M        ctn"M 

log  A  sin'^^ 

loj;  A    sin-M       | 

log  A     sin-M 

9.50 

.51 
.52 
.53 
.54 

9.55 
.56 
.57 

.58 
.59 

9.60 

.61 
.62 
.63 
.64 

9.65 
.66 
.67 
.68 
.69 

9.70 

.71 
.72 
.73 
.74 

9.75 
.76 
.77 

.78 
.79 

9.80 

.81 

.82 
.83 

.84 

9.85 
.86 

.87 
.88 
.89 

9.90 
.91 
.92 
.93 
.94 

9.95 
.96 
.97 

.98 
.99 

0.00 

O       /           /           Of 

18  26    2.6    71  34 

o        /           / 

17  33    2.3 

O         1 

72  27 

0.50 

.49 

.48 
.47 
.46 

0.45 
.44 
.43 
.42 
.41 

0.40 

.39 
.38 
.37 
.36 

0.35 

.34 
.33 
.32 
.31 

0.30 

.29 

.28 
.27 
.26 

0.25 
.24 
.23 
.22 
.21 

0.20 

.19 
.18 
.17 
.16 

0.15 

.14 
.13 
.12 
.11 

0.10 
.09 

.08 
.07 
.06 

0.05 

.04 
.03 
.02 
.01 

0.00 

9.750 

.755 
.760 
.765 
.770 

9.775 

.780 
.785 
.790 
.795 

9.800 
.805 
.810 
.815 
.820 

9.825 

.830 
.835 
.840 
.845 

9.850 
.852 

.854 
.856 

.858 

9.860 
.862 
.864 
.866 

.868 

9.870 

.872 
.874 
.876 

.878 

9.880 

.882 
.884 
.886 
.888 

9.890 
.891 
.892 
.893 
.894 

9.895 
.896 

.897 
.898 
.899 

9.900 

34  13 

1 

5.4 

9.900 

.901 
.902 
.903 
.904 

9.905 
.906 
.907 
.908 
.909 

9.910 

.911 
.912 
.913 
.914 

9.915 

.916 
.917 
.918 
.919 

9.920 
.921 
.922 
.923 
.924 

9.925 
.926 
.927 
.928 
.929 

9.930 
.931 
.932 
.933 
.934 

9.935 

.936 
.937 
.938 
.939 

9.940 
.941 
.942 
.943 
.944 

9.945 

.946 
.947 
.948 
.949 

9.950 

O        (            1 

52  36    10 

9.950 

.951 
.952 
.953 
.954 

9.955 
.956 
.957 
.958 
.959 

9.960 
.961 
.962 
.963 
.964 

9.965 
.966 
.967 
.968 
.969 

9.970 

.971 
.972 
.973 
.974 

9.975 
.976 
.977 

.978 
.979 

9.980 
.981 
.982 
.983 
.984 

9.985 
.986 
.987 

.988 
.989 

9.990 
.991 
.992 
.993 
.994 

9.995 
.996 
.997 
.998 
.999 

0.000 

O        1          / 

63  02    16 

18  53    2.7    71  07 

19  20    2.8    70  40 

19  48    2.9    70  12 

20  17    a.p    69  43 

17  56    2.3 

18  19     2.4 

18  43    2.4 

19  07    2.5 

72  04 
71  41 
71  17 
70  53 

34  40 

35  08 

35  36 

36  04 

6.6 
6.6 
6.7 
5,8 

52  46    10 

52  56    10 

53  07    11 
53  17    11 

63  17    16 
63  33    16 

63  49    16 

64  06    IB 

20  47    3.0    69  13 

19  32    2.5 

70  28 

30  34 

5.9 

53  28    u 

64  22    16 

21  17    3.1    68  43 

21  49    3.2    68  11 

22  21    3.3    67  39 
22  54    3.3    67  06 

19  57    2.5 

20  23    2.6 

20  49    2.6 

21  15     2.7 

70  03 
69  37 
69  11 
68  45 

37  03 

37  33 

38  04 
38  35 

6.0 
6.1 
6.2 
6.3 

53  39     11 

53  50     11 

54  00     11 
54  11     11 

04  39    17 

64  55     17 

65  12    17 
65  30    17 

23  28    3.4    66  32 

21  42    2.7 

68  18 

39  07 

6.4 

.54  22     11 

65  47     IS 

24  02    3.5    65  58 

24  38    3.6    65  22 

25  15    3.7    64  45 

25  53    3.8    64  07 

22  10    2.8 

22  38    2.8 

23  06    2.9 
23  35    2.9 

67  50 
67  22 
66  54 
66  25 

39  40 

40  13 

40  47 

41  21 

6.6 
6.7 
6.8 
7.0 

54  33    11 
54  45    11 

54  56    11 

55  07    11 

66  05    18 
66  23    18 

66  41     18 

67  00    19 

26  32    4.0    63  28 

24  04    2.9 

65  56 

41  56 

-.1 

55  19    11 

67  18    19 

27  12    4.1    62  48 

27  53    4.2    62  07 

28  36    4.3    61  24 

29  20    4.4    60  40 

24  34    3.0 

25  04    3.0 

25  35    3.1 

26  06    3.1 

65  26 
64  56 
64  25 
63  54 

42  32 

43  09 

43  47 

44  25 

7.3 

7.4 
7.6 
7.8 

55  30    12 
55  42    12 

55  53    12 

56  05    12 

67  37    19 

67  57    20 

68  16    20 
68  36    20 

30  05    4.6    59  55 

26  37    3.2 

63  23 

45  04 

7.9 

56  17    12 

68  57    21 

30  51    4.7    59  09 

31  39    4.9    58  21 

32  29    6.0    57  31 

33  20    ,1.2    56  40 

27  09    3.2 

27  41    3.3 

28  14    3.3 
28  47    3.3 

62  51 
62  19 
61  46 
61  13 

45  20 
45  36 

45  52 

46  09 

8.0 
8.1 
8.2 
8.2 

56  29    12 
56  41     12 

56  53    12 

57  05    12 

69  18    21 

69  39    SI 

70  00    22 
70  22    22 

34  13    r,.i    55  47 

29  21    3.4 

60  39 

46  25 

8  3 

57  17     12 

70  45    23 

35  08           54  52 

36  04           53  56 

37  03           52  57 

38  04           51  56 

29  55    3.4 

30  29    3.5 

31  04    3.5 
31  39    3.5 

60  05 
59  31 
58  56 
58  21 

46  42 

46  59 

47  16 
47  33 

3.4 
8.5 
8.6 

8.7 

57  30     12 
57  42     13 

57  55     13 

58  07     13 

71  08    23 

71    31      24 

71  55    94 

72  20    25 

39  07            50  53 

32  15    3.6 

57  45 

47  51 

8.7 

58  20     13 

72  45    25 

40  13            49  47 

41  21            48  39 

42  32           47  28 

43  47            46  13 

32  51    3.6 

33  27    3.6 

34  04    3.7 
34  41    3  7 

57  09 
56  33 
55  56 
55  19 

48  08 
48  26 

48  44 

49  02 

8.8 
8.9 
9.0 
9.1 

58  33     13 
58  46     13 

58  59    13 

59  12    13 

73  U    26 

73  37    27 

74  04    28 
74  33    29 

45  04            44  56 

35  18    3.7 

54  42 

49  20 

9.2 

59  26    13 

75  02    30 

46  25           43  35 

47  51            42  09 

49  20            40  40 

50  55            39  05 

35  55    3.8 

36  33    3.8 

37  11      3.8 

37  49    3  8 

54  05 
53  27 
52  49 
52  11 

49  39 

49  58 

50  17 
50  36 

9.3 
9.4 
9.5 
9.6 

59  39    14 

59  53    14 

60  06    14 
60  20    u 

75  32    31 
70  03    32 

76  36    33 

77  10    35 

52  36            37  24 

:$8  28    3.9 

51  32 

50  55 

9.7 

60  34    14 

77  45    36 

54  22           35  38 
56  17           33  43 
58  20           31  40 
60  34           29  26 

39  06    3.9 

39  45    3.9 

40  24    3.9 

41  03    3.9 

50  54 
50  15 
49  36 

48  .57 

51  05    9.8 
51  15    9.n 
51  25    9.9 
51  .35»io.o 

60  48     14 

61  03    14 
01  17     14 
61  31     n 

78  23    38 

79  02    41 

79  44    44 

80  30    47 

63  02           26  58 

41  43    .19 

48  17 

51  45 

in  0 

61  46     1.5 

81  19 

65  47           24  13 
68  57           21  03 
72  45           17  15 
77  45           12  15 

42  22    3.9 

43  01    3.9 

43  41    4.0 

44  20    4.0 

47  38 
46  59 
46  19 
45  40 

51  55 

52  05 
52  15 
52  25 

10.1 
10.2 
10.2 
10.3 

62  01     15 
02  16     15 
62  31     15 
62  46     15 

82  14 

83  16 

84  30 
86  07 

90  00             0  00 

oil          o       t 

45  00    4.0 

O       1          1 

45  00 

O        ' 

52  36 

o     / 

10.4 

1 

63  02     16 

90  00 

0        '          ' 

cac'^A       see 'A  ctur'A 

tan" '.4  log^ 

*  Beyond  this  point  the  uncertainty  i 

imounts  to  ±  0'.5. 

13 


TRAVERSE   TABLE. 


1 

2 
3 
4 

5' 

6 
7 
8 
9 

10" 

11 

12 
13 
14 

15' 

16 
17 
18 
19 

20^ 

21 
22 
23 
24 

25° 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35° 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45° 


diff  lat  =  dist .  cos  course. 

12     3     4     5     6     7     8 


1.00  2.00  3.00  4.00  5.00  6.00  7.00  8.00  9.00 


1.00  2.00  3.00  4.00 
1.00  2.00 1 3.00  4.00 
1.00  2.00  3.00  3.99 
1.00  2.00  2.99  3.99 


5.00 
5.00 
4.99 
4.99 


1.00   1.99  I  2.99  3.98  |4. 98 


0.99   1.9912.98  3.98 

0.99  1.9912.98  3.97 

0.99  1.98  2.97  3.96 

0.99  1.98  2.96  3.95 


0.98   1.97  1 2.95  3.94 


h'' 


0.98 
0.98 
0.97 
0.97 


1.96 
1.96 
1.95 
1.94 


2.94 
2.93 
2.92 
2.91 


3.93 
3.91 
3.90 

3.88 


0.97   1.93 


0.96 
0.96 
0.95 
0.95 


1.92 
1  91 
1.90 
1.89 


2.90  3.86 


2.88 
2.87 
2.85 
2.84 


3.85 
3.83 
3.80 
3.78 


0.94  1.: 


0.93 
0.93 
0.92 
0.91 


1.87 
1.85 
1.84 
1.83 


0.91    1.81 


0.90 
0.89 
0.88 
0.87 

air 


1.80 
1.78 
1.77 
1.75 


1.73 


0.86 
0.85 
0.84 
0.83 

0.82 


1.71 
1.70 
1.68 
1.66 


2.82  3.76 


2.80 
2.78 
2.76 
2.74 


3.73 
3.71 
3.68 
3.65 


2.72  3.63 


2.70 
2.67 
2.65 
2.62 


3.60 
3.56 
3.53 
3.50 


2.60  3.46 


2.57 
2.54 
2.52 
2.49 


3.43 
3.39 
3.35 
3.32 


4.97 
4.96 
4.95 
4.94 


4.92 


4.91 
4.89 

4.87 
4.85 


6.00  7.00 
6.00  7.00 
5.99  6.99 
5.99  6.98 


5.98  6.97 


8.00  9.00 
8.00  8.99 
7.99  8.99 
7.98  8.98 


7.97  8.97 


5.97  6.96  7.96  8.95 

5.96  6.95  7.94  8.93 

5.94  6.93  7.92  8.91 

5.93  6.91   7.90  8.89 


1.91   6.89 


5.89 
5.87 
5.85 
5.82 


6.87 
6.85 
6.82 
6.79 


4.83 


4.81 
4.78 
4.76 
4.73 


4.70 


4.67 
4.64 
4.60 
4.57 


4.53 


4.49 
4.46 
4.41 
4.37 


4.33 


29 
4.24 
4.19 
4.15 


l.C4|2.46  3.28  I  4.10 


5.80  6.76 


5.77 
5.74 
5.71 
5.67 


6.73 
6.69 
6.66 
6,62 


5.64  6.58 


5.60 
5.56 
5.52 
5.48 


6.54 
6.49 
6.44 
6.39 


5.44  6.34 


5.39 
5.35 
5.30 
5.25 


6.29 
6.24 
6.18 
6.12 


5.20  6.06 


5.14 
5.09 
5.03 
4.97 


6.00 
5.94 
5.87 
5.80 


7.88  8.86 


7.85 
7.83 
7.79 
7.76 


8.83 
8.80 
8.77 
8.73 


dep  =  dist .  sin  course. 
12     3     4     5     6     7 


8     9 


0.00  0.00  0.00  0.00  0.00  0.00  0.0010.00  0.00 


0.02  0.03 
0.03  0.07 
0.05  0.10 
0.07  0.14 


0.09  0.17 


0.10  0.21 
0.12  0.24 
0.14  0.28 
0.16  0.31 


0.17  0.35 


7.73  8.69 


7.69 
7.65 
7.61 
7.56 


8.65 
8.61 
8.56 
8.51 


7.52  8.46 


7.47 
7.42 
7.36 
7.31 


8.40 
8.34 
8.28 
8.22 


7.25  8.16 


7.19 
7.13 
7.06 
7.00 


8.09 
8.02 
7.95 

7.87 


6.93  7.79 


6.86 
6.78 
6.71 
6.63 


7.71 
7.63 
7..55 
7.46 


4.91    5.7;s   6.55   7.31 


0.81 
0.80 
0.79 
0.78 

ojt" 


1.62 
1.60 
1.58 
1.55 


1.53 


0.75 
0.74 
0.73 
0.72 


1.51 
1.49 
1.46 
1.44 


0.71    1.41 


2.43 
2.40 
2.36 
2.33 


3.24 
3.19 
3.15 
3.11 


2.30  3.06 


2.26 
2.23 
2.19 
2.16 


3.02 
2.97 
2.93 

2.88 


4.05 
3.99 
3.94 
3.89 


3.83 


3.77 
3.72 
3.66 
3.60 


2.12  2.83    3.54  4.24  4.95 


4.85 
4.79 
4.73 
4.66 


5.66 
5.59 
5.52 
5.44 


4.60  5.36 


4..53 
4.46 
4.39 
4.32 


5.28 
5.20 
5.12 
5.04 


6.47 
6.39 
6.30 
6.22 


7.28 
7.19 
7  09 
6.99 


6.13  6.89 


6.04 
5.95 
5.85 
5.75 


6.79 
6.69 
6.58 
6.47 


5.66  6.36 


1.00 
1.00 
0.99 


2.00 
1.99 
1.98 


3.00 
2.99 
2.97 


4.00U.99I5.99  6.99 
3.98  4.98  5.97  6.97 
3.96  4.95  5.94  6.92 


0.98   1.96 


0.97 
0.96 
0.94 


1.94 
1.91 

1.88 


0.92  1.85 


0.90 
0.88 
0.86 
0.83 


1.81 
1.76 
1.72 


1.66 


0.80 
0.77 
0.74 


1.61 
1.55 
1.48 


2.94  3.92 


2.91 

2.87 
2.82 


3.88 
3.83 
3.77 


2.77  3.70 


2.71 
2.65 
2.57 


3.62 
3.53 
3.43 


2.49  3.33 


2.41 
2.32 
2.22 


3.21 
3.09 
2.96 


4.90 


4.85 
4.78 
4.71 


4.62 


4.52 
4.41 
4.29 


4.16 


4.02 
3.87 
3.70 


5.88  6.87 


5.82  6.79 
5.74  6.70 
5.65  6.59 


5..54  6.47 


5.42  6.33 
5.29  6.17 
5.15  6.00 


4.99  5.82 


4.82  5.62 
4.64  5.41 
4.45  5.19 


7.99 
7.96 
7.91 


8.99 
8.96 
8.90 


7.85  8.83 


7.76 
7.66 
7.53 


8.73 
8.61 
8.47 


7.39  8.31 


7^3 
7.06 
6.86 


8.14 
7.94 
7.72 


6.65  7.48 


6.43 
6.18 
5.93 


7.23 
6.96 
6.67 


123456789 

dep  =  dist .  sin  course. 


0.19 
0.21 
0.22 
0.24 


0.38 
0.42 
0.45 
0.48 


0.26  0.52 


0.28 
0.29 
0.31 
0.33 


0.55 
0.58 
0.62 
0.65 


0.34  0.68 


0.36 
0.37 
0.39 
0.41 


0.72 
0.75 
0.78 
0.81 


0.42  0.85 


0.44 
0.45 
0.47 
0.48 


0.88 
0.91 
0.94 
0.97 


0.50  1.00 


0.52 
0  53 
0.54 
0.56 


1.03 
1.06 
1.09 
1.12 


0,05  0.07 
0.10  0.14 
0.16  0.21 
0.21  0.28 


0,09 
0.17 
0.26 
0.35 


0.10  0.12 
0.21  0.24 
0.31  0.37 
0.42  0.49 


0.26  0.35 1 0.44  1 0.52  0.61 


0.31  0.42 
0.37  0.49 
0.42  0.56 
0.47  0.63 


0.52 
0.61 1 
0.70 
0.78 


0.63  0.73 

0.73  0.85 

0.84  0.97 

0.94  1.10 


0.52  0.69 


0.57  0.76 
0.62  0.83 
0.67  0.90 
0.73  0.97 


0.78  1.04 


0.83  1.10 

0.88  1.17 

0.93  1.24 

0.98  1.30 


1.03  1.37 


1.08  1.43 
1.12  1.50 
1.17  1.56 
1.22  1.63 


1.27  1.69 


1.32  1,75 
1.36  1.82 
1.41  1.88 
1.45  1.94 


1.50  2.00 


1.55  2.06 
1.59  2.12 
1.63  2.18 
1.68  2.24 


0,57   1,15 


0.59 
0.60 
0.62 
0.63 


1.18 
1.20 
1.23 
1.26 


0.64  1.29 


Me 

0.67 
0.68 
0.69 


1.31 
1.34 
1.36 
1.39 


0.71    1.41 


1.72  2.29 


1.76  2.35 
1.81  2.41 
1.85  2.46 
1.89  2.52 


1.93  2.57 


1.97  2.62 

2.01  2.68 

2.05  2.73 

2.08  2.78 


2.12  2.83 


0.8; 


0.95 
1.04 
1.12 
1.21 


1.29 


1.38 
1.46 
1.55 
1.63 


1.71 


1.79 
1.87 
1.95 
2.03 


2.11 


2.19 
2.27 
2.35 
2.42 


2.50 


2.58 
2.65 
2.72 
2.80 


2.87 


2.94 
3.01 
3.08 
3.15 


3.21 


3.28 
3.35 
3.41 
3.47 


3.54 


1.04   1.22 


1.14  1.34 
1.25  1.46 
1.35  1.57 
1.45  1.69 


1.55   1.81 


1.65  1.93 
1.75  2.05 
1.85  2.16 
1,95  2.28 


2.05  2.39 


2.15  2.51 
2.25  2.62 
2.34  2.74 
2.44  2.85 


2.54  2.96 


2.63  3.07 
2.72  3.18 
2.82  3.29 
2.91   3.39 


3.00  3.50 


3.09  3.61 
3.18  3.71 
3.27  3.81 
3.36  3.91 


3.44  4.02 


3.53  4.11 
3.61  4.21 
3.69  4.31 
3.78  4.41 


3.86  4.50 


3.94  4.59 
4.01  4.68 
4.09  4.77 
4.17  4.86 


4.24  4.95 


0.14  0.16 
0.28  0.31 
0.42  0.47 
0.56  0.63 


0.70  0.78 


0.84  0.94 

0.97  1.10 

1.11  1.25 

1.25  1.41 


1..39   1.56 


1.53  1  72 
1.66  1.87 
1  80  2.02 
1.94  2.18 


2.07  2.33 


2.21  2.48 
2.34  2.63 
2.47  2.78 
2.60  2.93 


2.74  3,08 


2.87  3.23 
3.00  3.37 
3.13  3.52 
3.25  3.66 


3.38  3.80 


3.51  3.95 
3.63  4.09 
3.76  4.23 
3.88  4.36 


4.00  4.50 


4.12  4.64 

4.24  4.77 

4.36  4.90 

4.47  5.03 


4.59  5.1G 


4.70  5.29 

4.81  5.42 

4.93  5..54 

5.03  5,66 


5.14  5.79 


5.25  5.90 
5.35  6.02 
5.46  6.14 
5.56  6.25 


5.66  6.36 


0.05  0.10 
0.10  0.20 
0.15  0.29 


0.20  0.39 


0.24  0.4d 
0.29  0.58 
0.34  0.67 


0.38  0.77 


0.43  0.86 
0.47  0.94 
0.51  1.03 


0.56  1.11 


0.60  1.19 
0.63  1.27 
0.67  1.34 


0.15  0.20 
0.29  0.39 
0.44  0.59 


0.59  0.78 
0.73  0.97 


0.87 
1.01 


1.16 
1.35 


1,15  1.53 


1.28  1.71 
1.41  1.89 
1.54  2.06 


1.67  2.22 


1.79  2.38 
1.90  2.54 
2.01  2.69 


0.25 
0.49 
0.73 


0.98 


1.21 
1.45 
1.68 


1.91 


2.14 
2.36 
2.57 


2!Y8 


2.98 
3.17 
3.36 


0.29 
0.59 
0.88 


0.34 
0.69 
1.03 


1.17  1.37 


1.46 
1.74 
2.02 


1.70 
2.03 
2.36 


2.30  2.68 


2.57 
2.83 
3.08 


2.99 
3.30 
3.60 


3.33  3.89 


3.57 
3.81 
4.03 


4.17 
4.44 
4.70 


0.39  0.44 
0.78  0.88 
1.17  1.32 


1.56  1.76 


1.94  2.19 
2.32  2.61 
2.70  3.03 


3.06  3.44 


3.42  3.85 
3.77  4.24 
4.11  4.63 


4.44  5.00 


4.77  5..36 
5.08  5.71 
5.37  6.04 


123456789 

diflf  lat  =  dist .  cos  course. 
14 


w 

89 
88 
87 
86 

85* 

84 
83 
82 
81 

80° 

79 
78 
77 
76 

75° 

74 
73 
72 
71 

70° 

69 
68 
67 
66 

65° 

64 
63 
62 
61 

60° 

59 
58 
57 
56 

55° 

54 
53 
52 
51 

50° 

49 
48 
47 
46 

45° 


CoaaECTioN  op 

Middle  Latitude 

S.\iLiNa. 


•a 

3 


0° 

5 
10 
15 
20 
25 

26° 

27 

28 

29 

30 

31° 

32 

33 

34 

35 

36° 

37 

38 

39 

40 

41° 

42 

43 

44 

45 

46° 

47 

48 

49 

50 

51° 

52 

53 

54 

55 

56° 

57 

58 

59 

60 

61° 

62 

63 

64 

65 

66° 

67 

68 

69 

70 

71° 

72 

73 

74 

75 


Add  to  log 
sec,  or  sub- 
tract from 
tog  cos,  of 
mid  lat,  if 
diff  lat  o 
10». 


0.00055 
56 
59 
63 
70 
79 

0.00082 
84 
86 
89 
92 

0.00095 
098 
102 
106 
110 

0.00114 
118 
123 
128 
133 

0.00139 
145 
152 
159 
166 

0.00174 
183 
192 
202 
213 

0.00225 
238 
251 
266 
283 

0.00300 
320 
341 
365 
391 

0.00419 
451 
487 
527 
572 

0.00623 
681 
747 
823 
912 

0.01016 
1138 
1284 
1459 
1673 


For  a  given  mid 
lat,  the  correction 
nearly  propor- 
tional to  the  square 
o/the  diff  lat. 


1 

MERIDIONAL  PARTS. 

1 

0° 

10°  20°  30°  40°  50°  60°  70° 

80° 

85° 

87° 

89° 

0°oo' 

0 

603 

1225 

1888 

2623 

3474 

4527 

5966 

80°  00' 

8375 

85°  00' 

10765 

87°  00' 

12522 

89°  00' 

16300 

10 

10 

613 

1236 

1900 

36 

90 

47 

95 

05 

8404 

02 

788 

02 

561 

01 

357 

20 

20 

623 

46 

12 

49 

3506 

68 

6025 

10 

33 

04 

811 

04 

599 

02 

416 

30 

30 

634 

57 

23 

62 

21 

88 

55 

15 

63 

06 

834 

06 

639 

03 

476 

40 

40 

644 

68 

35 

75 

37 

4608 

85 

20 

92 

08 

858 

08 

678 

04 

537 

50 
I'OO' 

50 

654 

78 

46 

88 

53 

29 

6115 

25 
30' 

8522 
8552 

10' 
12 

10881 
905 

10' 
12 

12719 
759 

05' 
06 

16599 
662 

60 

664 

1289 

1958 

2702 

3569 

4649 

6146 

^H^ 

10 

70 

674 

1300 

70 

15 

85 

70 

77 

35 

83 

14 

929 

14 

801 

07 

726 

^^Bl 

20 

80 

684 

11 

81 

28 

3601 

91 

6208 

40 

8614 

16 

953 

16 

842 

08 

792 

^^hI 

30 

90 

695 

21 

93 

42 

17 

4712 

39 

45 

44 

18 

978 

18 

884 

09 

858 

■1 

40 

100 

705 

32 

2005 

55 

33 

33 

71 

50 

76 

20' 

11002 

20' 

12927 

10' 

16926 

50 

2«oo' 

110 

715 

43 

17 

68 

49 

54 

6303 

55 

81°  00' 

8707 

22 
24 

027 
052 

22 
24 

970 
13014 

11 
12 

996 
17067 

120 

725 

1354 

2028 

2782 

3665 

4775 

6335 

8739 

10 

130 

736 

64 

40 

95 

81 

96 

67 

05 

71 

26 

077 

26 

059 

13 

139 

20 

140 

746 

75 

52 

2809 

98 

4818 

6400 

10 

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^HM^Hi 

^^■HH 

^^■^^ 

15 


University  Press,  Cambridge  :  Printed  by  Welch,  Bigelow,  &  Co. 


I 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

This  book  is  DUE  on  the  last  date  stamped  below. 


50  cents  on  fourth  day  ovft^  .. 

One  dollar  on  seventh  day  overdue^,. 


OCT  20    134/ 

.-■-IT 


.^/l^^'i 


MAY  1 2 1955 


LD  21-100m-12,'46(A2012sl6)4120 


Stcckton, 


C«l»- 


T.l«''«« 


US.  pat.  Off 


4??364 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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